A213749 Antidiagonal sums of the convolution array A213747.

1, 9, 46, 180, 603, 1827, 5164, 13878, 35905, 90189, 221274, 532584, 1261687, 2949255, 6815896, 15597738, 35389629, 79691985, 178258150, 396361980, 876609811, 1929380139, 4227858756, 9227469150, 20065550713, 43486544277, 93952410034, 202400334288

Offset: 1

Author

Clark Kimberling, Jun 19 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 (9,-33,63,-66,36,-8).

Crossrefs

Cf. A213747, A213500.

Programs

Mathematica

(See A213747.)
LinearRecurrence[{9,-33,63,-66,36,-8},{1,9,46,180,603,1827},30] (* Harvey P. Dale, May 16 2013 *)

PARI

Vec(x*(1 - 2*x^2) / ((1 - x)^3*(1 - 2*x)^3) + O(x^30)) \\ Colin Barker, Oct 30 2017

Formula

a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6).

G.f.: x*(1 - 2*x^2) / ((1 - x)^3*(1 - 2*x)^3).

a(n) = (1/2)*((1+n)*(4-2^(2+n) + n + 2^(1+n)*n)). - Colin Barker, Oct 30 2017