A111990 Convolution of A111989 with itself.

1, 12, 108, 848, 6192, 43200, 292224, 1933056, 12572928, 80702464, 512532480, 3226742784, 20166803456, 125262102528, 773910872064, 4759428268032, 29151365234688, 177913041518592, 1082361265782784, 6565932190138368

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

W. Lang, Riccati meets Fibonacci, The Fibonacci Quarterly, 42 (2004) pp. 231-244, eqs.(58),(59).

Index entries for linear recurrences with constant coefficients, signature (12, -36, -16, 96, 0, -64).

Formula

G.f.: 1/(1-6*x+8*x^3)^2.

a(n) = (2*(n+1)*b(n+1)-(n+3)*b(n)-4*(n+2)*b(n-1))/9, with b(n):=A111989(n).

Mathematica

CoefficientList[Series[1/(1-6x+8x^3)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{12, -36, -16, 96, 0, -64}, {1, 12, 108, 848, 6192, 43200}, 30] (* Harvey P. Dale, Dec 07 2022 *)

Prog

(PARI) Vec(1/(1-6*x+8*x^3)^2 + O(x^30)) \\ Michel Marcus, Mar 11 2016

Crossrefs

Cf. A111991 (second convolution of A111989).

Sequence in context: A241230 A353047 A037972 * A053469 A055533 A037602

Adjacent sequences: A111987 A111988 A111989 * A111991 A111992 A111993

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 12 2005

Status

approved