A213823 Principal diagonal of the convolution array A213822.

4, 41, 147, 358, 710, 1239, 1981, 2972, 4248, 5845, 7799, 10146, 12922, 16163, 19905, 24184, 29036, 34497, 40603, 47390, 54894, 63151, 72197, 82068, 92800, 104429, 116991, 130522, 145058, 160635, 177289

Offset: 1

Author

Clark Kimberling, Jul 04 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. A213822.

Programs

Mathematica

(See A213822.)

Formula

a(n) = (-n - 3n^2 + 12*n^3)/2.

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*(4 + 25*x + 7*x^2) and g(x) = (1-x)^4.