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A111990
Convolution of A111989 with itself.
3
1, 12, 108, 848, 6192, 43200, 292224, 1933056, 12572928, 80702464, 512532480, 3226742784, 20166803456, 125262102528, 773910872064, 4759428268032, 29151365234688, 177913041518592, 1082361265782784, 6565932190138368
OFFSET
0,2
LINKS
W. Lang, Riccati meets Fibonacci, The Fibonacci Quarterly, 42 (2004) pp. 231-244, eqs.(58),(59).
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 12 2005
STATUS
approved