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A094286
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Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1.
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0
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1, 2, 4, 9, 21, 51, 127, 323, 835, 2187, 5787, 15435, 41419, 111659, 302059, 819243, 2226219, 6058155, 16503211, 44991659, 122727595, 334914219, 914235051, 2496201387, 6816678571, 18617371307, 50851322539, 138903833259
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,-6,-2,4).
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FORMULA
| a(n)=(1/12)*(4 + 3*2^n + (1-sqrt(3))^n + (1+sqrt(3))^n) = 1/3 +2^(n-2)+ A026150(n)/6.
G.f. -x*(1-3*x+3*x^3) / ( (x-1)*(2*x-1)*(2*x^2+2*x-1) ). - R. J. Mathar, Dec 20 2011
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MATHEMATICA
| LinearRecurrence[{5, -6, -2, 4}, {1, 2, 4, 9}, 30] (* From Harvey P. Dale, Feb 01 2012 *)
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CROSSREFS
| Sequence in context: A048285 A051529 A005207 * A094287 A094288 A168051
Adjacent sequences: A094283 A094284 A094285 * A094287 A094288 A094289
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KEYWORD
| easy,nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
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