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A063376
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a(-1) = 1; for n >= 0, a(n) = 2^n + 4^n = 2^n*(1+2^n).
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50
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1, 2, 6, 20, 72, 272, 1056, 4160, 16512, 65792, 262656, 1049600, 4196352, 16781312, 67117056, 268451840, 1073774592, 4295032832, 17180000256, 68719738880, 274878431232, 1099512676352, 4398048608256, 17592190238720, 70368752566272
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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COMMENTS
| Counts closed walks of length 2n+2 at a vertex of the cyclic graph on 8 nodes C_8.
The count of closed walks of odd length is zero. See the array w(N,L) and triangle a(K,N) given in A199571 for the general case. - Wolfdieter Lang, Nov 08 2011
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]
With offset 0 = binomial transform of A122983. [Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 18 2011]
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REFERENCES
| 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.)
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LINKS
| Harry J. Smith, Table of n, a(n) for n=-1,...,200
Index entries for sequences related to linear recurrences with constant coefficients, signature (6,-8).
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FORMULA
| 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.: 1/x + (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
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EXAMPLE
| a(1)=6 counts six round trips from, say, vertex no 1: 12121, 18181, 12181, 18121, 12321 and 18781. - Wolfdieter Lang, Nov 08 2011
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MAPLE
| seq(ceil(2^n*(2^n + 1)), n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 07 2008
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MATHEMATICA
| Table[2^n + 4^n, {n, 0, 25}]
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PROG
| (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]
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CROSSREFS
| Cf. A000051, A006516, A007582, A034472, A034474, A034491, A052539, A062394, A062395, A062396, A007689, A063376, A063481, A074600 - A074624, A122983.
Sequence in context: A049141 A049129 * A161168 A049139 A071356 A141200
Adjacent sequences: A063373 A063374 A063375 * A063377 A063378 A063379
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KEYWORD
| easy,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 14 2001
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EXTENSIONS
| 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
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