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A121990
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Binet A003215 type recursion with 3 instead of 2 as coeffiencient of a[n-1] and 12 nearest neighbors: a[n] = 3*a[n - 1] - a[n - 2] + 12.
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0
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1, 13, 50, 149, 409, 1090, 2873, 7541, 19762, 51757, 135521, 354818, 928945, 2432029, 6367154, 16669445, 43641193, 114254146, 299121257, 783109637, 2050207666, 5367513373, 14052332465, 36789484034, 96316119649, 252158874925
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a[n]=(1/10) (-120 + (65 - 11 Sqrt[5]) ((1/2) (3 - Sqrt[5]))^n + ((1/2) (3 + Sqrt[5]))^n (65 + 11 Sqrt[5]))
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FORMULA
| a(n) = 3*a[n - 1] - a[n - 2] + 12
a(n)=4*a(n-1)-4*a(n-2)+a(n-3). G.f.: -x*(1+9*x+2*x^2)/((x-1)*(x^2-3*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2009]
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MATHEMATICA
| f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == 3*a[n - 1] - a[n - 2] + 12, a[0] == 1, a[1] == 13}, a[n], n][[1]] // FullSimplify] a = Rationalize[N[Table[f[n], {n, 0, 25}], 100], 0]
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CROSSREFS
| Cf. A003215, A005891.
Sequence in context: A189054 A050410 A121991 * A050491 A022283 A135971
Adjacent sequences: A121987 A121988 A121989 * A121991 A121992 A121993
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 10 2006
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