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A024175
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Expansion of (x^3-6*x^2+5*x-1)/((2*x-1)*(2*x^2-4*x+1))
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7
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1, 1, 2, 5, 14, 42, 132, 428, 1416, 4744, 16016, 54320, 184736, 629280, 2145600, 7319744, 24979584, 85262464, 291057920, 993641216, 3392317952, 11581727232, 39541748736, 135002491904, 460924372992, 1573688313856, 5372896120832
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 8 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 1. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 11 2004
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 29 2010: (Start)
Counts all paths of length (2*n), n>=0, starting and ending at the initial node on the path graph P_7, see the Maple program.
(End)
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-10,4).
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FORMULA
| a(n)=(1/4)*Sum(r, 1, 7, Sin(r*Pi/8)^2(2Cos(r*Pi/8))^(2n)), n>=1 a(n)= 6a(n-1)-10a(n-2)+4a(n-3), n>=4 - Herbert Kociemba (kociemba(AT)t-online.de), Jun 11 2004
a(n)=(1/4)*((2+sqrt(2))^(n-1)+(2-sqrt(2))^(n-1)+2^n) for n>=1. [From Richard Choulet (richardchoulet(AT)yahoo.fr), Apr 19 2010]
a(n) = 2^(n-2) + A006012(n-1)/2, n>0. - R. J. Mathar, Mar 14 2011
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MAPLE
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 29 2010: (Start)
with(GraphTheory): G:=PathGraph(7): A:= AdjacencyMatrix(G): nmax:=26; n2:=2*nmax: for n from 0 to n2 do B(n):=A^n; a(n):=B(n)[1, 1]; od: seq(a(2*n), n=0..nmax);
(End)
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CROSSREFS
| Cf. A006012, A030436 and A094803.
Sequence in context: A061922 A162746 A148329 * A152226 A054393 A036768
Adjacent sequences: A024172 A024173 A024174 * A024176 A024177 A024178
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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