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A118808
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Number of partitions of n having exactly one part with multiplicity 3.
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1
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0, 0, 0, 1, 0, 1, 2, 3, 3, 5, 8, 13, 13, 23, 28, 40, 49, 71, 89, 123, 147, 198, 249, 329, 400, 518, 642, 825, 996, 1265, 1545, 1941, 2340, 2920, 3533, 4357, 5233, 6417, 7717, 9399, 11211, 13591, 16215, 19540, 23189, 27826, 32990, 39392, 46504, 55313, 65200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Column 1 of A118806.
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FORMULA
| G.f.=product([1-x^(3j)+x^(4j)]/(1-x^j), j=1..infinity)*sum(x^(3j)*(1-x^j)/[1-x^(3j)+x^(4j)], j=1..infinity).
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EXAMPLE
| a(9)=5 because we have [6,1,1,1],[4,2,1,1,1],[3,3,3],[3,3,1,1,1] and [3,2,2,2].
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MAPLE
| g:=product((1-x^(3*j)+x^(4*j))/(1-x^j), j=1..70)*sum(x^(3*j)*(1-x^j)/(1-x^(3*j)+x^(4*j)), j=1..70): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..60);
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MATHEMATICA
| Table[Length[Select[IntegerPartitions[n], Count[Length/@Split[#], 3]==1&]], {n, 0, 60}] (* From Harvey P. Dale, Mar 24 2011 *)
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CROSSREFS
| Cf. A118806, A118807, A116596.
Sequence in context: A017820 A129577 A107854 * A193979 A059503 A194000
Adjacent sequences: A118805 A118806 A118807 * A118809 A118810 A118811
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2006
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