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A176848
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Number of compositions of n into floor(j/3) kinds of j's for all j>=1.
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2
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1, 0, 0, 1, 1, 1, 3, 4, 5, 10, 15, 21, 36, 56, 83, 134, 210, 320, 505, 791, 1221, 1911, 2988, 4639, 7240, 11305, 17595, 27436, 42806, 66691, 103968, 162144, 252720, 393965, 614285, 957581, 1492791, 2327396, 3628273, 5656274, 8818275, 13747425, 21431700, 33411976, 52088551, 81204526, 126596778, 197361904, 307682405
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OFFSET
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0,7
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COMMENTS
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The g.f. for compositions of k_1 kinds of 1's, k_2 kinds of 2's, ..., k_j kinds of j's, ... is 1/(1-sum(j>=1, k_j * x^j )).
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LINKS
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FORMULA
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G.f.: 1/(1-sum(j>=1, floor(j/3)*x^j )).
Conjectural g.f.: (x-1)^2*(x^2+x+1) / (x^4-2*x^3-x+1). - Colin Barker, May 15 2013
G.f.: 1 + x^3*Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 + 2*x^2 - x^3)/( x*(4*k+3 + 2*x^2 - x^3 ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 11 2013
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PROG
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(PARI) N=66; x='x+O('x^N) /* that many terms */
gf= 1/(1-sum(j=1, N, floor(j/3)*x^j ))
Vec(gf) /* show terms */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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