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

Author

Gary W. Adamson, Oct 14 2007

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A134237.

Programs

Mathematica

LinearRecurrence[{3,-3,1},{1,5,14},50] (* or *) Rest[CoefficientList[Series[x*(2*x^2 + 2*x + 1)/(1-x)^3,{x,0,50}],x]] (* James C. McMahon, Apr 05 2025 *)

PARI

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

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)

Extensions

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