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A068980
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Number of partitions of n into nonzero tetrahedral numbers.
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32
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1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 11, 11, 12, 12, 15, 15, 16, 16, 19, 19, 22, 22, 25, 25, 28, 29, 32, 32, 35, 36, 42, 42, 45, 46, 52, 53, 56, 57, 63, 64, 70, 71, 77, 78, 84, 87, 94, 95, 101, 104, 115, 116, 122, 125, 136, 139, 146, 149, 160, 163, 175
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OFFSET
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0,5
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Zhicheng Gao, Andrew MacFie and Daniel Panario, Counting words by number of occurrences of some patterns, The Electronic Journal of Combinatorics, 18 (2011), #p143.
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FORMULA
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G.f.: 1 / prod(k>=3, 1 - z^binomial(k, 3) ).
G.f.: Sum_{i>=0} x^(i*(i+1)*(i+2)/6) / Product_{j=1..i} (1 - x^(j*(j+1)*(j+2)/6)). - Ilya Gutkovskiy, Jun 08 2017
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EXAMPLE
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a(10)=4 because we can write 10 = 10 = 4 + 4 + 1 + 1 = 4 + 1 + 1 + 1 + 1 + 1 = 1 + ... + 1.
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[1/(1-x^(k*(k+1)*(k+2)/6)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 09 2017 *)
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CROSSREFS
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See also A007294 (partitions into triangular numbers), A000292 (tetrahedral numbers).
Cf. A226748, A003108.
Sequence in context: A091372 A185322 A324918 * A280950 A279135 A053266
Adjacent sequences: A068977 A068978 A068979 * A068981 A068982 A068983
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters, Apr 01 2002
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STATUS
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approved
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