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

1,1

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).

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.

Mathematica

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

Crossrefs

Cf. A213841.

Sequence in context: A319219 A345687 A211224 * A221464 A119940 A004256

Adjacent sequences: A213842 A213843 A213844 * A213846 A213847 A213848

Keyword

nonn,easy

Author

Clark Kimberling, Jul 05 2012

Status

approved