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Search: id:A121991
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| A121991 |
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a(n) = 3*a(n-1) -a(n-2) -a(n-3) +12. |
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+0
1
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| 0, 1, 13, 50, 148, 393, 993, 2450, 5976, 14497, 35077, 84770, 204748, 494409, 1193721, 2882018, 6957936, 16798081, 40554301, 97906898, 236368324, 570643785, 1377656145, 3325956338, 8029569096, 19385094817
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OFFSET
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0,3
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COMMENT
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This result is same for 1, 13, 50 and one lower for the next term than the general Fibonacci type recursion.
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FORMULA
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a(n) = 3*a(n-1) -a(n-2) -a(n-3)+ 12.
a(n) = (-22 + (11 - 7 Sqrt[2])*(1 - Sqrt[2])^n + (1 + Sqrt[2])^n*(11 + 7 Sqrt[2]) - 24 n)/4 .
O.g.f.: -x(1+9x+2x^2)/((1-x)^2*(x^2+2x-1)) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2009
a(n)= -6(n+1)+(1+11*A000129(n+1)+3*A000129(n))/2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2009
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MATHEMATICA
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f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == 3*a[n - 1] - a[n - 2] - a[n - 3] + 12, a[0] == 0, a[1] == 1, a[2] == 13}, a[n], n][[1]] // FullSimplify] a = Rationalize[N[Table[f[n], {n, 0, 25}], 100], 0]
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CROSSREFS
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Cf. A003215, A005891.
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KEYWORD
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nonn,new
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 10 2006
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EXTENSIONS
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Edited by njas, Aug 24 2008
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