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A161078
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Number of partitions of n into primes or 1 where every part appears at least 3 times.
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1
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0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 6, 5, 6, 10, 8, 9, 14, 13, 16, 21, 19, 23, 30, 31, 34, 42, 44, 49, 60, 61, 68, 83, 85, 96, 111, 115, 129, 149, 158, 173, 196, 210, 229, 260, 275, 301, 339, 359, 392, 436, 462, 505, 559, 594, 645, 708, 755, 817, 895, 952, 1026, 1123, 1194, 1287
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OFFSET
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1,6
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LINKS
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FORMULA
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G.f.: -1+(1+x^3/(1-x))*product[1+x^{3*p(j)}/(1-x^{p(j)}, j=1..infinity], where p(j) is the j-th prime. - Emeric Deutsch, Jun 27 2009
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EXAMPLE
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a(12)=6 because we have 3333, 333111, 2^6, 22221111, 2221^6, and 1^(12). - Emeric Deutsch, Jun 27 2009
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MAPLE
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g := -1+(1+x^3/(1-x))*(product(1+x^(3*ithprime(j))/(1-x^ithprime(j)), j = 1 .. 20)): gser := series(g, x = 0, 75): seq(coeff(gser, x, n), n = 2 .. 65); # Emeric Deutsch, Jun 27 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition edited to "primes or 1" by R. H. Hardin, Jun 22 2009
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STATUS
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approved
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