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)gmail.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

For n>0: A000120(a(n))=2, A023414(a(n))=2*(n-1), A087117(a(n))=n-1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 23 2009]

a(n+1) written in base 2: 11, 1010, 100100, 10001000, 1000010000, ..., i.e. number 1, n times 0, number 1, n times 0 (A163449(n)). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 27 2009]

a(n) for n >= 1 is a bisection of A001445(n+1). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 14 2009]

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

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

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]

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

Index entries for sequences related to linear recurrences with constant coefficients

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

a(n)= A000079(n)+A006516(n). - Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 06 2008

a(n) = A028403(n+1) / 4. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 27 2009]

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 (simon.plouffe(AT)gmail.com)