A213830 Antidiagonal sums of the convolution array A213828.

2, 18, 78, 230, 540, 1092, 1988, 3348, 5310, 8030, 11682, 16458, 22568, 30240, 39720, 51272, 65178, 81738, 101270, 124110, 150612, 181148, 216108, 255900, 300950, 351702, 408618, 472178, 542880, 621240

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. A213828.

Programs

Mathematica

(See A213828.)
LinearRecurrence[{5,-10,10,-5,1},{2,18,78,230,540},30] (* Harvey P. Dale, Jan 11 2015 *)

Formula

a(n) = (2*n + n^2 + 2*n^3 + 3*n^4)/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*(1 + 4*x + 4*x^2) and g(x) = (1-x)^5.