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Search: id:A111178
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| A111178 |
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Number of partitions of n into positive numbers one less than a square. |
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+0
2
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| 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 4, 5, 2, 5, 5, 2, 6, 7, 4, 6, 7, 5, 6, 8, 6, 8, 12, 6, 9, 13, 6, 10, 15, 8, 14, 15, 9, 16, 16, 10, 18, 21, 14, 19, 22, 16, 20, 24, 19, 25, 30, 20, 27, 33, 21, 29, 39, 26, 37, 40, 28, 42, 42, 31, 48
(list; graph; listen)
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OFFSET
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0,16
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COMMENT
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Also limiting form of the number of representations of n into k positive squares for k decreasing from n to 1, or Table[Count[SumOfSquaresRepresentations[k,n], {a_,__}/;a>0], {n,100,100},{k,100,40,-1}]. (Franklin T. Adams-Watters: replacing k^2 ones by the value k^2 changes the count by k^2-1).
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FORMULA
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product(k=1..inf, 1/(1-x^(k^2-1)))
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MATHEMATICA
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Product[1/(1-x^(k^2-1)), {k, 2, 100}]
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CROSSREFS
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Cf. A001156, A078134.
Sequence in context: A025432 A025433 A025434 this_sequence A076845 A016014 A067760
Adjacent sequences: A111175 A111176 A111177 this_sequence A111179 A111180 A111181
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KEYWORD
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easy,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 22 2005
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