0,3

a(n) is the sum of the maximum(m,n) over {(m,n):m,n in positive integers,m<=n} [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Oct 11 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 2.

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

I. Siap, Linear codes over F_2 + u*F_2 and their complete weight enumerators, in Codes and Designs (Ohio State, May 18, 2000), pp. 259-271. De Gruyter, 2002.

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

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.

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

a(n) = n*(n+1)*(4*n-1)/6. G.f.: x*(1+3*x)/(1-x)^4.

n^3-sum(i^2, i=1..(n-1)) - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de).

Partial sums of n odd triangular numbers, e.g. a(3)=t(1)+t(3)+t(5)=1+6+15=22 - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003

a(n)=sum(i=0, n-1, (n-i)(n+i)) - Jon Perry (perry(AT)globalnet.co.uk), Sep 26 2004

Binomial transform of (1, 6, 9, 4, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 16 2007

a(n) = n*A000292(n) - (n-1)*A000292(n-1) = n*C((n+2),3) - (n-1)*C((n+1),3); e.g. a(5) = 95 = 5*35 - 4*20. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2007

seq(add((n^2-k^2), k=0..n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 02 2006

a:=n->sum(binomial(n+j, 1)*binomial(n-j, 1), j=0..n): seq(a(n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 02 2006

A002412:=z*(1+3*z)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]

f[n_]:=4*n+1; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]

(PARI) v=vector(40, i, t(i)); s=0; forstep(i=1, 40, 2, s+=v[i]; print1(s", "))

Bisection of A002623. Equals A000578(n)-A000330(n-1).

Cf. A016061.

a(n)= A093561(n+2, 3), (4, 1)-Pascal column.

Cf. A000292.

Sequence in context: A010001 A014073 A129109 this_sequence A041215 A060822 A011926

Adjacent sequences: A002409 A002410 A002411 this_sequence A002413 A002414 A002415

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

Plouffe Maple line edited by R. J. Mathar, May 16 2008