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 A068980 Number of partitions of n into nonzero tetrahedral numbers. 22
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS 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. FORMULA 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 EXAMPLE a(10)=4 because we can write 10 = 10 = 4 + 4 + 1 + 1 = 4 + 1 + 1 + 1 + 1 + 1 = 1 + ... + 1. MATHEMATICA 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 *) CROSSREFS 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 KEYWORD easy,nonn AUTHOR Franklin T. Adams-Watters, Apr 01 2002 STATUS approved

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)