A213782 Principal diagonal of the convolution array A213781.

1, 7, 19, 41, 72, 118, 176, 254, 347, 465, 601, 767, 954, 1176, 1422, 1708, 2021, 2379, 2767, 3205, 3676, 4202, 4764, 5386, 6047, 6773, 7541, 8379, 9262, 10220, 11226, 12312, 13449, 14671, 15947, 17313, 18736, 20254, 21832, 23510, 25251, 27097, 29009, 31031

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 (2,1,-4,1,2,-1).

Crossrefs

Cf. A213781, A213500.

Programs

Mathematica

(See A213781.)
LinearRecurrence[{2,1,-4,1,2,-1},{1,7,19,41,72,118},50] (* Harvey P. Dale, Oct 17 2016 *)

PARI

Vec(x*(1+5*x+4*x^2-2*x^4)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 31 2016

Formula

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

G.f.: x*(1+5*x+4*x^2-2*x^4) / ((1-x)^4*(1+x)^2). - Corrected by Colin Barker, Jan 31 2016

From Colin Barker, Jan 31 2016: (Start)

a(n) = (16*n^3+66*n^2+6*(-1)^n*n-34*n-3*(-1)^n+3)/48.

a(n) = (8*n^3+33*n^2-14*n)/24 for n even.

a(n) = (8*n^3+33*n^2-20*n+3)/24 for n odd.

(End)