0,2

-2, -4, -6, -8, -10, -12, -14, ... are the trivial zeros of the Riemann zeta function. - Vivek Suri (vsuri(AT)jhu.edu), Jan 24 2008

Numbers of carbons in the oligomers of acetylene. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Oct 27 2005

Excluding the first two terms, this sequenc is the same as the number of carbons in the oligomers of cyclobutane sharing a common edge. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Apr 05 2006

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 2-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 19 2007

A134452(a(n)) = 0; A134451(a(n)) = 2 for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2007

Omitting the initial zero gives the number of prime divisors with multiplicity of product of terms of n-th row of A077553. - Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 21 2003

A059841(a(n))=1, A000035(a(n))=0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 29 2008]

Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Oct 28 2008: (Start)

(APSO) Alternating partial sums of

(a-b+c-d+e-f+g...)=(a+b+c+d+e+f+g...)-2*(b+d+f...)

it appears that APSO A005843 =

A052928 = A002378 - 2*(A116471)

A116471=2*A008794

(End)

If A=[A157872] 9*n.^2-3 (6, 33, 78, 141,.,); Y=[A005843] 2*n (except the first term , 2,4,6,8,.,); X=[A140811] 6*n^2-1 (except the first term, 5,23,5395,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 5^2-6 *2^2=1; 23^2-33*4^2=1; 53^2-78*6^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009]

A056753(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2009]

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

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

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Kevin Fagan, Drabble cartoon, Jun 15 1987: Intelligence Test

Milan Janjic, Two Enumerative Functions

Tanya Khovanova, Recursive Sequences

Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009]

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.

Eric Weisstein's World of Mathematics, Hamiltonian Circuit

Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.

Edward Everett Withford, Pell Equation [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009]

Index entries for "core" sequences

Index entries for sequences related to linear recurrences with constant coefficients

G.f.: 2*x/(1-x)^2.

Inverse binomial transform of A036289, n*2^n. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jan 13 2006

a(0)=0, a(1)=2, a(n)=2a(n-1)-a(n-2). - Jaume Oliver i Lafont (joliverlafont(AT)gmail.com), May 07 2008

a(n)=Sum{k=1,n}floor(6n/4^k+1/2) [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 04 2009]

a(n) = A034856(n+1) - A000124(n) = A000217(n) + A005408(n) - A000124(n) = A005408(n) - 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009]

A005843 := n->2*n;

A005843:=2/(z-1)**2; [S. Plouffe in his 1992 dissertation.]

lst={}; Do[AppendTo[lst, 2*n], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 29 2008]

(MAGMA) [ 2*n : n in [0..100]];

(R) seq(0, 200, 2)

(PARI) A005843(n) = 2*n

Cf. A000027, A005408.

Cf. A001358, A005843, A077553, A077554, A077555, A002024, A087112.

Cf. A157872, A140811 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009]

easy,core,nonn,nice

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