A213850 Antidiagonal sums of the convolution array A213849.

1, 3, 10, 20, 42, 70, 120, 180, 275, 385, 546, 728, 980, 1260, 1632, 2040, 2565, 3135, 3850, 4620, 5566, 6578, 7800, 9100, 10647, 12285, 14210, 16240, 18600, 21080, 23936, 26928, 30345, 33915, 37962, 42180, 46930

Offset: 1

Author

Clark Kimberling, Jul 05 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Crossrefs

Cf. A213849.

Programs

Mathematica

(See A213849.)

Formula

a(n) = (n + 1)*(n + 2)*(3 - 3*(-1)^n + 8*n + 2*n^2)/96.

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) = x*(1 + x + 2*x^2) and g(x) = (1+x)^3*(1-x)^5.