0,2

Let G_n be the elementary abelian group G_n = (C_2)^n for n >= 1: A006516 is the number of times the number -1 appears in the character table of G_n and A007582 is the number of times the number 1. Together the two sequences cover all the values in the table i.e. A006516(n) + A007582(n) = 2^(2n). - Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 01 2001

Number of walks of length 2n+1 between two adjacent vertices in the cycle graph C_8. Example: a(1)=3 because in the cycle ABCDEFGH we have three walks of length 3 between A and B: ABAB, ABCB, and AHAB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

Smallest number containing in its binary representation two equal non-overlapping subwords of length n: A097295(a(n))=n and A097295(m)<n for m<a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 04 2004

a(n)^2 + (A006516(n))^2 = a(2n). E.g. a(3) = 36, A006516(3) = 28, a(6) = 2080. 36^2 + 28^2 = 2080. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 17 2006

Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either x equals y or x does not equal y. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 02 2008

Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A). This is just a simpler statement of my previous comment for this sequence. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008

S. Hong and J. H. Kwak, Regular fourfold covering with respect to the identity automorphism, J. Graph Theory, 17 (1993), 621-627.

T. D. Noe, Table of n, a(n) for n=0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 168

G.f.: (1-3*x)/((1-2*x)*(1-4*x)). C(1+2^n, 2) where C(n, 2) is n-th triangular number A000217.

Binomial transform of A007051. Inverse binomial transform of A081186. - Paul Barry (pbarry(AT)wit.ie), Apr 07 2003

E.g.f. exp(3x)cosh(x) - Paul Barry (pbarry(AT)wit.ie), Apr 07 2003

a(n)=sum{k=0..floor(n/2); C(n, 2k)3^(n-2k) } - Paul Barry (pbarry(AT)wit.ie), May 08 2003

a(n+1) = 4*a(n) - 2^n; see also A049775. a(n) = 2^(n-1)*A000051(n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 2004

a(n)=6a(n-1)-8a(n-2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

Row sums of triangle A134308 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007

a(n) = StirlingS2(2^n + 1,2^n) = 1 + 2*StirlingS2(n+1,2) + 3*StirlingS2(n+1,3) + 3*StirlingS2(n+1,4) = StirlingS2(n+2,2) + 3(StirlingS2(n+1,3) + StirlingS2(n+1,4)). - Ross La Haye (rlahaye(AT)new.rr.com), Mar 01 2008

a(n) = StirlingS2(2^n + 1,2^n) = 1 + 2*StirlingS2(n+1,2) + 3*StirlingS2(n+1,3) + 3*StirlingS2(n+1,4) = StirlingS2(n+2,2) + 3(StirlingS2(n+1,3) + StirlingS2(n+1,4)). - Ross La Haye (rlahaye(AT)new.rr.com), Apr 02 2008 Ross

seq(binomial(-2^n, 2), n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008

Table[ Binomial[2^n + 1, 2], {n, 0, 23}] (from Robert G. Wilson v Jul 30 2004)

(PARI) a(n)=if(n<0, 0, 2^(n-1)*(1+2^n))

(PARI) a(n)=sum(k=-n\4, n\4, binomial(2*n+1, n+1+4*k))

Cf. A000217, A049773, A049775.

Cf. A006516.

Cf. A134308.

Cf. A000225, A000392, A032263, a028243, A000079.

Sequence in context: A081909 A126189 A122448 this_sequence A026854 A136576 A129156

Adjacent sequences: A007579 A007580 A007581 this_sequence A007583 A007584 A007585

nonn,easy,nice

Simon Plouffe (plouffe(AT)math.uqam.ca)