A134238 Row sums of triangle A134237.

1, 5, 14, 28, 47, 71, 100, 134, 173, 217, 266, 320, 379, 443, 512, 586, 665, 749, 838, 932, 1031, 1135, 1244, 1358, 1477, 1601, 1730, 1864, 2003, 2147, 2296, 2450, 2609, 2773, 2942, 3116, 3295, 3479, 3668, 3862, 4061, 4265, 4474, 4688, 4907, 5131, 5360, 5594, 5833, 6077

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

Binomial transform of (1, 4, 5, 0, 0, 0, ...).

a(n) = a(n-1) + 5*n - 6 (with a(1)=1). - Vincenzo Librandi, Nov 23 2010

a(n) = (5*n^2 - 7*n + 4)/2. - Charles R Greathouse IV, Jun 17 2017

From Elmo R. Oliveira, Feb 08 2025: (Start)

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

E.g.f.: exp(x)*(5*x^2 - 2*x + 4)/2 - 2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)

Prog

(PARI) a(n)=(5*n^2-7*n+4)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A134237.

Sequence in context: A055454 A301294 A073347 * A024800 A005586 A197058

Adjacent sequences: A134235 A134236 A134237 * A134239 A134240 A134241

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 14 2007

Extensions

a(47) onwards from Andrew Howroyd, Feb 08 2025

Status

approved