Search: id:A007000
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%I A007000 M1045
%S A007000 1,2,4,7,11,17,25,35,49,66,88,115,148,189,238,297,368,451,550,665,799,
%T A007000 956,1136,1344,1583,1855,2167,2520,2920,3373,3882,4455,5097,5814,6617,
%U A007000 7509,8502,9604,10823,12173,13662,15302,17110,19093,21271,23657,26266
%N A007000 Number of partitions of n into Fibonacci parts (with 2 types of 1).
%D A007000 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007000 T. D. Noe, <a href="b007000.txt">Table of n, a(n) for n=0..1000</a>
%F A007000 a(n)=1/n*Sum_{k=1..n} (A005092(k)+1)*a(n-k), n > 1, a(0)=1. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Aug 22 2002
%F A007000 G.f.=1/product(1-x^fibonacci(j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 05 2006
%e A007000 a(2)=4 because we have [2],[1',1'],[1',1],[1,1] (the two types of 1 are 
               denoted 1 and 1').
%p A007000 with(combinat): gf := 1/product((1-q^fibonacci(k)), k=1..20): s := series(gf, 
               q, 200): for i from 0 to 199 do printf(`%d,`,coeff(s, q, i)) od:
%t A007000 CoefficientList[ Series[ 1/Product[1 - x^Fibonacci[i], {i, 1, 15}], {x, 
               0, 50}], x]
%Y A007000 Cf. A003107.
%Y A007000 Sequence in context: A028291 A067997 A034379 this_sequence A073472 A096914 
               A004250
%Y A007000 Adjacent sequences: A006997 A006998 A006999 this_sequence A007001 A007002 
               A007003
%K A007000 nonn
%O A007000 0,2
%A A007000 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
%E A007000 More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), 
               Feb 08, 2002

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