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

0,2

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).

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)

Example

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).

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 *)

Prog

(GAP) a:=List(List([0..32], n->List([0..n], k->Binomial(n, k)+n)), Sum); # Muniru A Asiru, Jul 17 2018
(PARI) Vec((1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Jul 18 2018

Crossrefs

Cf. A131923.

Sequence in context: A008059 A145132 A063758 * A143982 A000749 A360046

Adjacent sequences: A131921 A131922 A131923 * A131925 A131926 A131927

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 29 2007

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, May 07 2010

Status

approved