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

1,2

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A213781, A213500.

Sequence in context: A087762 A195349 A160422 * A269428 A097240 A097241

Adjacent sequences: A213779 A213780 A213781 * A213783 A213784 A213785

Keyword

nonn,easy

Author

Clark Kimberling, Jun 22 2012

Status

approved