0,3

Zero followed by partial sums of A005408 (odd numbers). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Aug 13 2002

Begin with n, add the next number, subtract the previous number and so on ending with subtracting a 1: a(n) = n + (n+1) - (n-1) +(n+2) -(n-2) +(n+3)-(n-3)...+(2n-1)-1 = n^2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2004

Sum of two consecutive triangular numbers A000217. - Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2004

Numbers with an odd number of divisors: {d(n^2)=A048691(n); for the first occurrence of 2n+1 divisors, see A071571(n)}. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 30 2004

First sequence ever computed by electronic computer, on EDSAC, May 6 1949 (see Renwick link). - Russ Cox (rsc(AT)swtch.com), Apr 20 2006

Numbers n such that the imaginary quadratic field Q[Sqrt[ -n]] has four units. - Marc LeBrun (mlb(AT)well.com), Apr 12 2006

Number of permutations of n distinct letters (ABCD...) each of which appears twice with two and n-2 fixed points. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 09 2006

For n>0: number of divisors of (n-1)th power of any squarefree semiprime: a(n)=A000005(A006881(k)^(n-1)); a(n) = A000005(A000400(n-1)) = A000005(A011557(n-1)) = A000005(A001023(n-1)) = A000005(A001024(n-1)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007

For n>=1, a(n) is equal to the number of functions f:{1,2}->{1,2,...,n} such that for y_1, y_2 in {1,2,...,n} we have f(1)<>y_1 and f(2)<>y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 17 2007

If a 2-set Y and an (n-2)-set Z are disjoint subsets of an n-set X then a(n-2) is the number of 3-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 19 2007

Also numbers a such that a^1/2 + b^1/2 = c^1/2 and a^2 + b = c. - Cino Hilliard (hillcino368(AT)hotmail.com), Feb 07 2008

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.

G. L. Alexanderson et al., The William Lowell Putnam Mathematical Competition, Problems and Solutions:1965-1984, "December 1967 Problem B4(a)", pp. 8(157) MAA Washington DC 1985.

R. P. Burn & A. Chetwynd, A Cascade Of Numbers, "The prison door problem" Problem 4 pp. 5-7;79-80 Arnold London 1996.

M. Gardner, Time Travel and Other Mathematical Bewilderments, Chapter 6 pp. 71-2, W.H.Freeman NY 1988.

A. S. Posamentier, The Art of Problem Solving, Section 2.4 "The Long Cell Block" pp. 10-1;12;156-7 Corwin Press Thousand Oaks CA 1996.

J. K. Strayer, Elementary Number Theory, Exercise Set 3.3 Problems 32;33 pp. 88 PWS Publishing Co. Boston MA 1996.

C. W. Trigg, Mathematical Quickies, "The Lucky Prisoners" Problem 141 pp. 40;141 Dover NY 1985.

R. Vakil, A Mathematical Mosaic, "The Painted Lockers" pp. 127;134 Brendan Kelly Burlington Ontario 1996.

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

Franklin T. Adams-Watters, The first 10000 squares: Table of n, n^2 for n = 0..10000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Milan Janjic, Two Enumerative Functions

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

H. Bottomley, Some Smarandache-type multiplicative sequences

J. Derbyshire, Monkeys and Doors

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 338

Hyun Kwang Kim, On Regular Polytope Numbers

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

W. S. Renwick, EDSAC log.

J. Scholes, 28th Putnam 1967 Prob.B4(a)

James A. Sellers, Partitions Excluding Specific Polygonal Numbers As Parts, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.

N. J. A. Sloane, Illustration of initial terms of A000217, A000290, A000326

D. Surendran, Chimbumu and Chickwama get out of jail

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

Eric Weisstein's World of Mathematics, Unit

Index entries for "core" sequences

Eric Weisstein's World of Mathematics, Wiener Index

Multiplicative with a(p^e) = p^(2e). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

G.f.: x(1+x)/(1-x)^3. E.g.f.: exp(x)(x+x^2). Dirichlet g.f.: zeta(s-2). a(n)=a(-n).

Sum of all matrix elements M(i, j) = 2*i/(i+j) (i, j = 1..n). a(n) = Sum[Sum[2*i/(i+j), {i, 1, n}], {j, 1, n}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 24 2004

a(0)=0, a(1)=1, a(n)=2*a(n-1)-a(n-2)+2 - Miklos Kristof (kristmikl(AT)freemail.hu), Mar 09 2005

a(n)=sum of the odd numbers for i=1 to n. a(0)=0 a(1)=1 then a(n)=a(n-1)+2*n-1. - Pierre CAMI (pierrecami(AT)tele2.fr), Oct 22 2006

For n>0: a(n) = A130064(n)*A130065(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2007

a(n) = Sum(A002024(n,k): 1<=k<=n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 24 2007

Left edge of the triangle in A132111: a(n)=A132111(n,0). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2007

a(n) = {least common multiple of n and n-1} - (n-1). - Mats Granvik (mgranvik(AT)abo.fi), Sep 16 2007

Binomial transform of [1, 3, 2, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 21 2007

a(n) = C(n+1,2) + C(n,2)

A000290 := n->n^2;

A000290:=-(1+z)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]

a[n_] := n^2; Table[a[n], {n, 0, 50}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 30 2006

Array[ #^2 &, 60, 0] - Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 26 2006

(MAGMA) [ n^2 : n in [0..1000]];

(PARI) a(n)=n^2

Cf. A092205.

Cf. A128200, A005408, A128201.

A row or column of A132191.

Adjacent sequences: A000287 A000288 A000289 this_sequence A000291 A000292 A000293

Sequence in context: A106545 A093837 A069821 this_sequence A018885 A025741 A030476

nonn,core,easy,nice,mult

njas