A213760 Antidiagonal sums of the convolution array A213783.

1, 4, 12, 27, 52, 92, 148, 230, 335, 480, 656, 889, 1162, 1512, 1912, 2412, 2973, 3660, 4420, 5335, 6336, 7524, 8812, 10322, 11947, 13832, 15848, 18165, 20630, 23440, 26416, 29784, 33337, 37332, 41532, 46227, 51148, 56620, 62340, 68670

Offset: 1

Author

Clark Kimberling, Jun 22 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 (2,2,-6,0,6,-2,-2,1).

Crossrefs

Cf. A213783, A213500.

Programs

Mathematica

(See A213783.)
LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{1,4,12,27,52,92,148,230},40] (* Harvey P. Dale, Feb 13 2024 *)

PARI

Vec(x*(1 + x - x^2)*(1 + x + 2*x^2) / ((1 - x)^5*(1 + x)^3) + O(x^60)) \\ Colin Barker, May 04 2017

Formula

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) -2*a(n-7) +a(n-8).

G.f.: f(x)/g(x), where f(x) = x*(1 + 2*x + 2*x^2 + x^3 -2*x^4) and g(x) = (1 + x)^3 *(1 - x)^5.

From Colin Barker, May 04 2017: (Start)

a(n) = (2*n^4 + 22*n^3 + 40*n^2 + 8*n) / 96 for n even.

a(n) = (2*n^4 + 22*n^3 + 34*n^2 + 26*n + 12) / 96 for n odd.

(End)