A131403 Row sums of triangle A131402.

1, 2, 5, 10, 21, 44, 93, 196, 411, 856, 1771, 3642, 7451, 15178, 30809, 62358, 125921, 253800, 510777, 1026704, 2061751, 4137012, 8295895, 16627190, 33311671, 66716054, 133582133, 267407026, 535206861, 1071049316, 2143127061, 4287918172, 8578528851, 17161414288

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (5, -8, 3, 3, -2)

Formula

From Andrew Howroyd, Aug 09 2018: (Start)

a(n) = 5*a(n-1) - 8*a(n-2) + 3*a(n-3) + 3*a(n-4) - 2*a(n-5).

G.f.: (1 - 3*x + 3*x^2 - 2*x^3 + 2*x^4)/((1 - x)^2*(1 - 2*x)*(1 - x - x^2)).

(End)

Example

a(4) = 21 = sum of row 4 terms of A131402: (1 + 6 + 7 + 6 + 1).

Mathematica

LinearRecurrence[{5, -8, 3, 3, -2}, {1, 2, 5, 10, 21}, 40] (* Harvey P. Dale, Nov 22 2021 *)

Prog

(PARI) Vec((1 - 3*x + 3*x^2 - 2*x^3 + 2*x^4)/((1 - x)^2*(1 - 2*x)*(1 - x - x^2)) + O(x^40)) \\ Andrew Howroyd, Aug 09 2018

Crossrefs

Cf. A131402.

Sequence in context: A066819 A114279 A101400 * A264544 A052540 A018106

Adjacent sequences: A131400 A131401 A131402 * A131404 A131405 A131406

Keyword

nonn

Author

Gary W. Adamson, Jul 07 2007

Extensions

Terms a(10) and beyond from Andrew Howroyd, Aug 09 2018

Status

approved