Search: id:A063376
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%I A063376
%S A063376 1,2,6,20,72,272,1056,4160,16512,65792,262656,1049600,4196352,16781312,
%T A063376 67117056,268451840,1073774592,4295032832,17180000256,68719738880,
%U A063376 274878431232,1099512676352,4398048608256,17592190238720,70368752566272
%N A063376 a(-1) = 1; for n >= 0, a(n) = 2^n + 4^n = 2^n*(1+2^n)..
%C A063376 Counts closed walks of length 2n+2 at a vertex of the cyclic graph on 
               8 nodes C_8.
%C A063376 Number of monic irreducible polynomials of degree 1 in GF(2^n)[x,y]. 
               - Max Alekseyev (maxale(AT)gmail.com), Jan 23 2006
%C A063376 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]
%D A063376 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.)
%H A063376 Harry J. Smith, <a href="b063376.txt">Table of n, a(n) for n=-1,...,200</
               a>
%H A063376 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A063376 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
%F A063376 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)).
%F A063376 a(n)=ceil(2^n*(2^n + 1)),n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 07 2008
%p A063376 seq(ceil(2^n*(2^n + 1)),n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 07 2008
%t A063376 Table[2^n + 4^n, {n, 0, 25}]
%o A063376 (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]
%Y A063376 Cf. A007582, A006516.
%Y A063376 Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, 
               A007689, A063376, A063481, A074600 - A074624.
%Y A063376 Sequence in context: A150133 A049141 A049129 this_sequence A161168 A049139 
               A071356
%Y A063376 Adjacent sequences: A063373 A063374 A063375 this_sequence A063377 A063378 
               A063379
%K A063376 easy,nonn
%O A063376 -1,2
%A A063376 Henry Bottomley (se16(AT)btinternet.com), Jul 14 2001
%E A063376 Entry rewritten by N. J. A. Sloane (njas(AT)research.att.com) Jan 23 
               2006
%E A063376 Definition corrected to a(-1) = 1; by Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Aug 20 2009

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