A213779 Principal diagonal of the convolution array A213778.

1, 6, 15, 33, 58, 97, 146, 214, 295, 400, 521, 671, 840, 1043, 1268, 1532, 1821, 2154, 2515, 2925, 3366, 3861, 4390, 4978, 5603, 6292, 7021, 7819, 8660, 9575, 10536, 11576, 12665, 13838, 15063, 16377, 17746, 19209, 20730, 22350, 24031, 25816, 27665, 29623

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

Crossrefs

Cf. A213778, A213500.

Programs

Mathematica

(See A213778.)
LinearRecurrence[{2,1,-4,1,2,-1},{1,6,15,33,58,97},80] (* Harvey P. Dale, Dec 12 2016 *)

PARI

Vec(x*(1+4*x+2*x^2+x^3)/((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+4*x+2*x^2+x^3) / ((1-x)^4*(1+x)^2).

From Colin Barker, Jan 31 2016: (Start)

a(n) = (16*n^3+30*n^2+2*(3*(-1)^n+7)*n+3*((-1)^n-1))/48.

a(n) = (8*n^3+15*n^2+10*n)/24 for n even.

a(n) = (8*n^3+15*n^2+4*n-3)/24 for n odd.

(End)