-1,2

Counts closed walks of length 2n+2 at a vertex of the cyclic graph on 8 nodes C_8.

Number of monic irreducible polynomials of degree 1 in GF(2^n)[x,y]. - Max Alekseyev (maxale(AT)gmail.com), Jan 23 2006

a(n) written in base 2: a(-1) = 1, a(0) = 10, a(n) for n >= 1: 110, 10100, 1001000, 100010000, ..., i.e. number 1, (n-1) times 0, number 1, n times 0 (see A163664). a(n) for n >= 0 is duplicate of A161168. a(n) for n >= 0 is a bisection of A005418. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 14 2009]

J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13. (See Table 11.)

Harry J. Smith, Table of n, a(n) for n=-1,...,200

Index entries for sequences related to linear recurrences with constant coefficients

G.f.: (1-4x+x^2)/((1-2x)(1-4x)); a(n)=sum{k=0..n, if(mod(n-k, 4)=0, binomial(n, 2k), 0)}. - Paul Barry (pbarry(AT)wit.ie), Sep 19 2005

a(n) = 4a(n-1)-2^n = 6a(n-1)-8a(n-2) = A001576(n)-1 = 2*A007582(n) = A005418(2n+2) = A002378(A000079(n)). G.f.: (2-6*x)/((1-2*x)*(1-4*x)).

a(n)=ceil(2^n*(2^n + 1)),n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 07 2008

seq(ceil(2^n*(2^n + 1)), n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 07 2008

Table[2^n + 4^n, {n, 0, 25}]

(PARI) { for (n = -1, 200, if (n>=0, p=2^n; a=p*(1 + p), a=1); write("b063376.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 20 2009]

Cf. A007582, A006516.

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.

Sequence in context: A150133 A049141 A049129 this_sequence A161168 A049139 A071356

Adjacent sequences: A063373 A063374 A063375 this_sequence A063377 A063378 A063379

easy,nonn

Henry Bottomley (se16(AT)btinternet.com), Jul 14 2001

Entry rewritten by N. J. A. Sloane (njas(AT)research.att.com) Jan 23 2006

Definition corrected to a(-1) = 1; by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 20 2009