A131951 a(n) = 2^n + n*(n+3).

1, 6, 14, 26, 44, 72, 118, 198, 344, 620, 1154, 2202, 4276, 8400, 16622, 33038, 65840, 131412, 262522, 524706, 1049036, 2097656, 4194854, 8389206, 16777864, 33555132, 67109618, 134218538, 268436324, 536871840, 1073742814, 2147484702, 4294968416, 8589935780

Offset: 0

Author

Gary W. Adamson, Jul 30 2007

Keywords

• nonn
• easy

Comments

Row sums of triangle A131950.

Examples

			a(3) = 26 = sum of row 3 terms, triangle A131950: (7 + 6 + 6 + 7).
a(3) = 26 = (1, 3, 3, 1) dot (1, 5, 3, 1) = (1 + 15 + 9 + 1).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Crossrefs

Cf. A131950.

Programs

Mathematica

LinearRecurrence[{5,-9,7,-2},{1, 6, 14, 26},34] (* James C. McMahon, Mar 02 2025 *)

Formula

Binomial transform of (1, 5, 3, 1, 1, 1, ...).

G.f.: ( 1+x-7*x^2+3*x^3 ) / ( (2*x-1)*(x-1)^3 ). - R. J. Mathar, Apr 04 2012

E.g.f.: exp(x)*(exp(x) + x*(4 + x)). - Stefano Spezia, Mar 03 2025

Extensions

New definition by R. J. Mathar, Apr 04 2012

a(28)-a(34) from James C. McMahon, Mar 02 2025