A213755 Antidiagonal sums of the convolution array A213753.

1, 9, 44, 160, 491, 1355, 3486, 8546, 20245, 46773, 106048, 236980, 523535, 1145935, 2489202, 5372534, 11532633, 24639513, 52426420, 111146280, 234877811, 494924179, 1040183174, 2181033290, 4563397341, 9529452605

Offset: 1

Author

Clark Kimberling, Jun 20 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-26,44,-41,20,-4).

Crossrefs

Cf. A213753, A213500.

Programs

Mathematica

(See A213753.)

Formula

a(n) = (1/6)*(84 - 21*2^(n+2) + 23*n + 9*n*2^(n+2) - 3*n^2 - 2*n^3).

a(n) = 8*a(n-1) - 26*a(n-2) + 44*a(n-3) - 41*a(n-4) + 20*a(n-5) - 4*a(n-6).

G.f.: f(x)/g(x), where f(x) = x*(1 + x - 2*x^2 - 2*x^3) and g(x) = (1 - x)^4 * (1 - 2*x)^2.