A213824 Antidiagonal sums of the convolution array A213822.

4, 30, 114, 310, 690, 1344, 2380, 3924, 6120, 9130, 13134, 18330, 24934, 33180, 43320, 55624, 70380, 87894, 108490, 132510, 160314, 192280, 228804, 270300, 317200, 369954, 429030, 494914, 568110, 649140

Offset: 1

Author

Clark Kimberling, Jul 04 2012

Keywords

• nonn
• easy

Comments

Every term is even.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A213822.

Programs

Mathematica

(See A213822.)

PARI

a(n) = n*(3*n^3 + 6*n^2 + 5*n + 2)/4 \\ Charles R Greathouse IV, Feb 09 2017

Formula

a(n) = (2*n + 5*n^2 + 6*n^3 + 3*n^4)/4 = n*(1 + n)*(2 + 3*n + 3*n^2)/4.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: f(x)/g(x), where f(x) = 2*x*(2 + 5*x + 2*x^2) and g(x) = (1-x)^5.

a(n) = Sum_{i=1..n} i*(3*i^2+1). - Bruno Berselli, Feb 09 2017