Search: id:A066258
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%I A066258
%S A066258 1,2,12,45,200,832,3549,14994,63580,269225,1140624,4831488,20466953,
%T A066258 86698690,367262700,1555747893,6590256856,27916771136,118257348165,
%U A066258 500946152850,2122041977276,8989114033297,38078498156832
%N A066258 Fibonacci(n)^2 * Fibonacci(n+1).
%D A066258 D. Zeitlin, Generating Functions for Products of Recursive Sequences, 
               Transactions A.M.S., 116, Apr. 1965, p. 304.
%F A066258 O.g.f.: (x-x^2)/(1-3x-6x^2+3x^3+x^4).
%F A066258 a(n) = second term from right in M^(n+1) * [1 0 0 0}, where M = the 4 
               X 4 upper Pascal's triangular matrix [1 3 3 1 / 1 2 1 0 / 1 1 0 0 
               / 1 0 0 0]. E.g. a(3) = 45 since M^4 * [1 0 0 0] = [125 75 45 27] 
               where 125 = A056570(5), 75 = A066259(4) and 27 = A056570(4). - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004
%F A066258 a(n) = (1/5) {F(3n+1) - (-1)^nF(n+2) }. - Ralf Stephan, Jul 26 2005
%Y A066258 Cf. A065563, A066259, A000045.
%Y A066258 Cf. A056570, A066259.
%Y A066258 First differences of A001655.
%Y A066258 Sequence in context: A025495 A028570 A009074 this_sequence A123771 A046991 
               A061990
%Y A066258 Adjacent sequences: A066255 A066256 A066257 this_sequence A066259 A066260 
               A066261
%K A066258 nonn
%O A066258 0,2
%A A066258 Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 09 2001

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