A213780 Antidiagonal sums of the convolution array A213778.

1, 6, 17, 40, 78, 140, 230, 360, 535, 770, 1071, 1456, 1932, 2520, 3228, 4080, 5085, 6270, 7645, 9240, 11066, 13156, 15522, 18200, 21203, 24570, 28315, 32480, 37080, 42160, 47736, 53856, 60537, 67830, 75753, 84360, 93670, 103740, 114590

Offset: 1

Author

Clark Kimberling, Jun 21 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 (3,-1,-5,5,1,-3,1).

Crossrefs

Cf. A213778, A213500.

Programs

Mathematica

(See A213778.)

Formula

a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).

G.f.: f(x)/g(x), where f(x) = x*(1 + 3*x) and g(x) = (1 + x)^2 *(1 - x)^5.