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A003404 Number of solid partitions of n supported on graph of cube.
(Formerly M3310)
4
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; text; internal format)
OFFSET

0,3

REFERENCES

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. [The g.f. shown below appears on page 121. - N. J. A. Sloane, Apr 22 2015]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Matthew House, Table of n, a(n) for n = 0..10000

G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 14.

G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, Europ. J. Combin., 22 (2001), 887-904.

Index entries for sequences related to posets

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-1,0,-1,0,1,2,1,0,1,-1,-1,-2,-1,-1,1,0,1,2,1,0,-1,0,-1,0,-1,0,0,1,1,-1).

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)).

MATHEMATICA

CoefficientList[Series[(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)), {q, 0, 40}], q] (* Harvey P. Dale, Mar 07 2012 *)

CROSSREFS

Cf. A003402, A003403, A003405, A029073, A256975, A256976, A256977.

Sequence in context: A008370 A291877 A048241 * A139025 A221107 A128610

Adjacent sequences:  A003401 A003402 A003403 * A003405 A003406 A003407

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 27 15:29 EDT 2021. Contains 346307 sequences. (Running on oeis4.)