A131253 Row sums of triangle A131252.

1, 3, 8, 17, 34, 64, 117, 209, 368, 641, 1108, 1904, 3257, 5551, 9432, 15985, 27030, 45616, 76845, 129245, 217056, 364033, 609768, 1020192, 1705009, 2846619, 4748072, 7912529, 13174858, 21919456, 36440613, 60538409, 100503632, 166744961, 276476092, 458151440

Offset: 0

Author

Gary W. Adamson, Jun 23 2007

Keywords

• nonn

Examples

			a(3) = 17 = sum of row 3 terms of A131252: (7 + 6 + 3 + 1).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (4, -4, -2, 4, 0, -1)

Crossrefs

Row sums of A131252.

Programs

Magma

I:=[1,3,8,17,34,64]; [n le 6 select I[n] else 4*Self(n-1)- 4*Self(n-2)-2*Self(n-3)+4*Self(n-4)-Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 10 2018

Mathematica

LinearRecurrence[{4, -4, -2, 4, 0, -1}, {1, 3, 8, 17, 34, 64}, 40] (* Vincenzo Librandi, Aug 10 2018 *)

PARI

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

PARI

a(n)={sum(k=0, n, (k+1)*sum(i=0, k, binomial(n-k, k-i)))} \\ Andrew Howroyd, Aug 09 2018

Formula

From Andrew Howroyd, Aug 09 2018: (Start)

a(n) = Sum_{k=0..n} (k+1)*(Sum_{i=0..k} binomial(n-k, k-i)).

a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6).

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

(End)

Extensions

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