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A003404
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Number of solid partitions of n supported on graph of cube.
(Formerly M3310)
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0
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1, 1, 4, 7, 14, 23, 41, 63, 104, 152, 230, 327, 470, 647, 897, 1202, 1616, 2117, 2775, 3566, 4580, 5787, 7301, 9092, 11298, 13885, 17028, 20688, 25076, 30154, 36172, 43094, 51221, 60511, 71323, 83622, 97822, 113893, 132323, 153083
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, Europ. J. Combin., 22 (2001), 887-904.
P. A. MacMahon, Memoir on the theory of partitions of numbers - Part VI, Phil. Trans. Roal Soc., 211 (1912), 345-373 (see Section 98).
J. C. P. Miller, On the enumeration of partially ordered sets of integers, pp. 109-124 of T. P. McDonough and V. C. Mavron, editors, Combinatorics: Proceedings of the Fourth British Combinatorial Conference 1973. London Mathematical Society, Lecture Note Series, Number 13, Cambridge University Press, NY, 1974.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 14.
Index entries for sequences related to posets
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FORMULA
| G.f.: (1 + 2*q^2 + 2*q^3 + 3*q^4 + 3*q^5 + 5*q^6 + 4*q^7 + 8*q^8 + 4*q^9 + 5*q^10 + 3*q^11 + 3*q^12 + 2*q^13 + 2*q^14 + q^16)/((1 - q)*(1 - q^2)*(1 - q^3)*(1 - q^4)*(1 - q^5)*(1 - q^6)*(1 - q^7)*(1 - q^8)).
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CROSSREFS
| Sequence in context: A146417 A008370 A048241 * A139025 A128610 A094968
Adjacent sequences: A003401 A003402 A003403 * A003405 A003406 A003407
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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