A131924 Row sums of triangle A131923.

1, 4, 10, 20, 36, 62, 106, 184, 328, 602, 1134, 2180, 4252, 8374, 16594, 33008, 65808, 131378, 262486, 524668, 1048996, 2097614, 4194810, 8389160, 16777816, 33555082, 67109566, 134218484, 268436268, 536871782, 1073742754, 2147484640

Offset: 0

Author

Gary W. Adamson, Jul 29 2007

Keywords

• nonn
• easy

Examples

			a(4) = 36 = sum of terms in row 4 of triangle A131923: (5 + 8 + 10 + 8 + 5).
a(4) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..600
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Crossrefs

Cf. A131923.

Programs

GAP

a:=List(List([0..32],n->List([0..n],k->Binomial(n,k)+n)),Sum); # Muniru A Asiru, Jul 17 2018

Mathematica

Table[2^n + n^2 + n, {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, May 07 2010 *)
LinearRecurrence[{5,-9,7,-2},{1,4,10,20},40] (* Harvey P. Dale, Jul 22 2021 *)

PARI

Vec((1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Jul 18 2018

Formula

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

a(n) = 2^n + n^2 + n. - Michel Marcus, Jul 18 2018

From Colin Barker, Jul 18 2018: (Start)

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

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>3.

(End)

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, May 07 2010