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A213787
a(n) = Sum_{1<=i<j<k<=n} F(i)*F(j)*F(k), where F(m) is the m-th Fibonacci number.
5
0, 0, 0, 2, 17, 102, 518, 2442, 11010, 48444, 209979, 902132, 3854708, 16416204, 69769244, 296148174, 1256077725, 5324954250, 22567665834, 95626443110, 405154147310, 1716454353240, 7271524823255, 30804002164872, 130491325800072, 552779233930872, 2341634254967448, 9919384305913082, 42019349641680905
OFFSET
0,4
LINKS
Index entries for linear recurrences with constant coefficients, signature (6, -2, -29, 16, 40, -11, -14, 2, 1).
FORMULA
G.f.: (x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)). - Alois P. Heinz, Jun 20 2012
MAPLE
a:= n-> (Matrix(9, (i, j)-> `if`(i=j-1, 1, `if`(i=9,
[1, 2, -14, -11, 40, 16, -29, -2, 6][j], 0)))^(n+3).
<<0, -1, 0, 0, 0, 0, 2, 17, 102>>)[1, 1]:
seq (a(n), n=0..30); # Alois P. Heinz, Jun 20 2012
MATHEMATICA
LinearRecurrence[{6, -2, -29, 16, 40, -11, -14, 2, 1}, {0, 0, 0, 2, 17, 102, 518, 2442, 11010}, 30] (* Jean-François Alcover, Feb 13 2016 *)
PROG
(PARI) x='x+O('x^50); concat([0, 0, 0], Vec((x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)))) \\ G. C. Greubel, Mar 05 2017
CROSSREFS
Sequence in context: A119363 A272065 A129977 * A105652 A204238 A198796
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 20 2012
STATUS
approved