A213832 Principal diagonal of the convolution array A213831.

1, 19, 78, 202, 415, 741, 1204, 1828, 2637, 3655, 4906, 6414, 8203, 10297, 12720, 15496, 18649, 22203, 26182, 30610, 35511, 40909, 46828, 53292, 60325, 67951, 76194, 85078, 94627, 104865, 115816, 127504

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. A213831.

Programs

Mathematica

(See A213831.)

Formula

G.f.: x*(1 + 15*x + 8*x^2)/(1-x)^4.

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

a(n) = (n - 7*n^2 + 8*n^3)/2.

a(n) = Sum_{i = 0..n-1} (n + i)*(n + 3*i). - Bruno Berselli, Feb 14 2018