A213839 Principal diagonal of the convolution array A213838.

1, 20, 89, 240, 505, 916, 1505, 2304, 3345, 4660, 6281, 8240, 10569, 13300, 16465, 20096, 24225, 28884, 34105, 39920, 46361, 53460, 61249, 69760, 79025, 89076, 99945, 111664, 124265, 137780, 152241, 167680

Offset: 1

Author

Clark Kimberling, Jul 05 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 (4,-6,4,-1).

Crossrefs

Cf. A213838.

Programs

Mathematica

(See A213838.)
LinearRecurrence[{4,-6,4,-1},{1,20,89,240},40] (* Harvey P. Dale, Mar 10 2013 *)

Formula

a(n) = (8*n - 21*n^2 + 16*n^3)/3.

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

G.f.: f(x)/g(x), where f(x) = x*(1 + 16*x + 15*x^2) and g(x) = (1-x)^4.