A121968 a(n) = 2*a(n-1) - a(n-2) + n + 1.

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

Offset

1,2

Comments

Equals binomial transform of [1, 1, 3, 1, 0, 0, 0, ...]. - Gary W. Adamson, Aug 25 2010

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

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 - 2*x + 4*x^2 - 2*x^3)/(1 - x)^4. - Robert G. Wilson v, Sep 11 2006

Mathematica

a[n_] := (6 + n(-1 + n(6 + n)))/6; Table[a[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, Sep 11 2006 *)

Prog

(PARI) x='x+O('x^50); Vec((1-2*x+4*x^2-2*x^3)/(1-x)^4) \\ G. C. Greubel, Sep 13 2017

Crossrefs

Cf. cake numbers A000125.

Sequence in context: A182155 A101586 A178080 * A305329 A161212 A256058

Adjacent sequences: A121965 A121966 A121967 * A121969 A121970 A121971

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 04 2006

Extensions

Edited and extended by Robert G. Wilson v, Sep 11 2006

Status

approved