A213845 Principal diagonal of the convolution array A213844.

3, 32, 119, 296, 595, 1048, 1687, 2544, 3651, 5040, 6743, 8792, 11219, 14056, 17335, 21088, 25347, 30144, 35511, 41480, 48083, 55352, 63319, 72016, 81475, 91728, 102807, 114744, 127571, 141320, 156023, 171712

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. A213841.

Programs

Mathematica

(See A213841.)
LinearRecurrence[{4,-6,4,-1},{3,32,119,296},40] (* Harvey P. Dale, Nov 06 2014 *)

Formula

a(n) = (2*n - 9*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*(3 + 20*x + 9*x^2) and g(x) = (1-x)^4.