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

1,2

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+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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A213778, A213500.

Sequence in context: A118734 A200895 A225278 * A051410 A083052 A333959

Adjacent sequences: A213776 A213777 A213778 * A213780 A213781 A213782

Keyword

nonn,easy

Author

Clark Kimberling, Jun 21 2012

Status

approved