A213764 Antidiagonal sums of the convolution array A213762.

1, 8, 31, 90, 225, 516, 1123, 2366, 4885, 9960, 20151, 40578, 81481, 163340, 327115, 654726, 1310013, 2620656, 5242015, 10484810, 20970481, 41941908, 83884851, 167770830, 335542885, 671087096, 1342175623, 2684352786

Offset: 1

Author

Clark Kimberling, Jun 20 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 (5,-9,7,-2).

Crossrefs

Cf. A213762, A213500.

Programs

Mathematica

(See A213762.)
LinearRecurrence[{5,-9,7,-2},{1,8,31,90},30] (* Harvey P. Dale, Jan 27 2016 *)

Formula

a(n) = -10 + 5*2^(n+1) - 7*n - 2*n^2.

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

G.f.: f(x)/g(x), where f(x) = x*(1 + 3*x) and g(x) = (1 - 2*x)*(1 - x)^3.