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A066259 a(n) = Fibonacci(n)*Fibonacci(n+1)^2. 8
1, 4, 18, 75, 320, 1352, 5733, 24276, 102850, 435655, 1845504, 7817616, 33116057, 140281700, 594243090, 2517253683, 10663258432, 45170286424, 191344405725, 810547906740, 3433536036866, 14544692047439, 61612304237568 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
D. Zeitlin, Generating Functions for Products of Recursive Sequences, Transactions A.M.S., 116, Apr. 1965, p. 304.
FORMULA
O.g.f.: (x+x^2)/(1-3x-6x^2+3x^3+x^4) = x(1+x)/((1+x-x^2)(1-4x-x^2)).
a(n) = second term from left in M^n * [1 0 0 0] where M = the 4 X 4 upper triangular Pascal's triangle matrix [1 3 3 1 / 1 2 1 0 / 1 1 0 0 / 1 0 0 0]. E.g., a(4) = 75 since M^4 * [1 0 0 0] = [125 75 45 27] = [A056570(5) a(4) A066258(3) A056570(4)]. - Gary W. Adamson, Oct 31 2004
a(n) = (1/5)*(F(3n+2) - (-1)^n*F(n-1)). - Ralf Stephan, Jul 26 2005
a(n) = (F(n+2)^3 - 2*F(n)^3 - F(n-1)^3)/6. - Greg Dresden, Aug 12 2022
MATHEMATICA
First[#]Last[#]^2&/@Partition[Fibonacci[Range[30]], 2, 1] (* Harvey P. Dale, Mar 04 2011 *)
PROG
(PARI) { for (n=1, 200, a=fibonacci(n) * fibonacci(n+1)^2; write("b066259.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 07 2010
CROSSREFS
Sequence in context: A180140 A245127 A037674 * A172159 A084213 A048664
KEYWORD
nonn,easy
AUTHOR
Len Smiley, Dec 09 2001
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)