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A067593
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Number of partitions of n into Lucas parts (A000032).
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5
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1, 1, 2, 3, 5, 6, 9, 12, 16, 20, 26, 33, 41, 50, 62, 75, 90, 107, 129, 151, 178, 208, 244, 281, 326, 375, 431, 491, 561, 638, 723, 816, 922, 1037, 1163, 1302, 1458, 1624, 1808, 2009, 2231, 2467, 2729, 3012, 3321, 3651, 4014, 4406, 4828, 5282, 5777, 6308, 6877, 7491, 8155, 8862, 9622, 10438, 11316, 12247, 13249
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: 1/((1-x^2)*prod(i>=1, 1-x^(fibonacci(i-1)+fibonacci(i+1)) ) ). - Emeric Deutsch, Mar 23 2005
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EXAMPLE
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a(5)=6 because we have 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1 and 1+1+1+1+1.
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PROG
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(PARI) N=66; q='q+O('q^N);
L(n) = fibonacci(n+1) + fibonacci(n-1);
gf = 1; k=0; while( L(k) <= N, gf*=(1-q^L(k)); k+=1 ); gf = 1/gf;
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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