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A121968
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a(n) = 2*a(n - 1) - a(n - 2) + n + 1.
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1
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1, 2, 6, 14, 27, 46, 72, 106, 149, 202, 266, 342, 431, 534, 652, 786, 937, 1106, 1294, 1502, 1731, 1982, 2256, 2554, 2877, 3226, 3602, 4006, 4439, 4902, 5396, 5922, 6481, 7074, 7702, 8366, 9067, 9806, 10584, 11402, 12261, 13162, 14106, 15094, 16127
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equals binomial transform of [1, 1, 3, 1, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 25 2010]
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FORMULA
| a(n) = (6 + n(-1 + n(6 + n)))/6 = C(n+1, 3) + n^2 + 1 = C(n+2, 3) + C(n, 2) + 1.
G.f. (1 - 2x + 4x^2 - 2x^3)/(x - 1)^4. - Robert G. Wilson v
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MATHEMATICA
| f[n_] := (6 + n(-1 + n(6 + n)))/6; Table[f[n], {n, 0, 45}] (* or *)
a[0] = 1; a[1] = 2; a[n_] := a[n] = 2a[n - 1] - a[n - 2] + n + 1; Table[ a[n], {n, 0, 45}] (* or *)
CoefficientList[ Series[(1 - 2x + 4x^2 - 2x^3)/(x - 1)^4, {x, 0, 45}], x] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. cake numbers A000125.
Sequence in context: A068041 A101586 A178080 * A161212 A033547 A050531
Adjacent sequences: A121965 A121966 A121967 * A121969 A121970 A121971
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 04 2006
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EXTENSIONS
| Edited and extended by Robert G. Wilson v Sep 11 2006
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