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

1,2

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) = (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.

Mathematica

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

Crossrefs

Cf. A213838.

Sequence in context: A306987 A249983 A234258 * A264302 A220200 A242656

Adjacent sequences: A213836 A213837 A213838 * A213840 A213841 A213842

Keyword

nonn,easy

Author

Clark Kimberling, Jul 05 2012

Status

approved