A132074 Row sums of triangle A132073.

1, 4, 9, 16, 27, 46, 81, 148, 279, 538, 1053, 2080, 4131, 8230, 16425, 32812, 65583, 131122, 262197, 524344, 1048635, 2097214, 4194369, 8388676, 16777287, 33554506, 67108941, 134217808, 268435539, 536870998, 1073741913, 2147483740

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2). [From R. J. Mathar, May 21 2010]

Formula

Binomial transform of [1, 3, 2, 0, 2, 0, 2, 0, 2, ...].

From R. J. Mathar, May 21 2010: (Start)

G.f.:= (2*x^2 + 2*x^3 - 1)/((2*x-1)*(x-1)^2).

a(n) = 2^n + 3*n - 1, n > 0. (End)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 06 2012

Example

a(4) = 27 = sum of row 4 terms of triangle A132073: (5 + 5 + 7 + 5 + 5).
a(4) = 27 = (1, 4, 6, 4, 1) dot (1, 3, 2, 0, 2) = (1 + 12 + 12 + 0 + 2).

Mathematica

CoefficientList[Series[(2*x^2+2*x^3-1)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)

Prog

(Magma) I:=[1, 4, 9, 16]; [n le 4 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 06 2012

Crossrefs

Cf. A132073.

Sequence in context: A029896 A301198 A009862 * A283549 A137354 A113495

Adjacent sequences: A132071 A132072 A132073 * A132075 A132076 A132077

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 09 2007

Extensions

More terms from R. J. Mathar, May 21 2010

Status

approved