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1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025, 196418
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All a(n) are Fibonacci numbers A000045[n]: a(2n-1) = Fibonacci[n], a(2n) = Fibonacci[n+2], a(2n-1) = a(2n+2). - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 08 2006
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,1)
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FORMULA
| a(n) = Fibonacci[A028242[n+2]]. a(n) = Fibonacci[A030451[n+1]] = Fibonacci[3/4 -(-1)^(n+1)*3/4 +(n+1)/2]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 08 2006
a(n) = A053602(n+1) = A097594(n-5). - R. J. Mathar, Mar 08 2011
G.f. -x*(1+2*x+x^3) / ( -1+x^2+x^4 ). - R. J. Mathar, Mar 08 2011
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MATHEMATICA
| p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n + 1)p[k - 2, x]; Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 20}]
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CROSSREFS
| Cf. A051792, A000045, A028242, A030451.
Sequence in context: A132091 A051792 A053602 * A058736 A097451 A005916
Adjacent sequences: A123228 A123229 A123230 * A123232 A123233 A123234
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 06 2006
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EXTENSIONS
| More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 08 2006
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