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]

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

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

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Two Enumerative Functions

Tanya Khovanova, Recursive Sequences

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.

Tanya Khovanova, Recursive Sequences

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.

Index entries for "core" sequences

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

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

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]

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]];

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]

Adjacent sequences: A005840 A005841 A005842 this_sequence A005844 A005845 A005846

Sequence in context: A087113 A004275 A119432 this_sequence A076032 A004277 A122080

easy,core,nonn,nice

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