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%I M3310 #31 Jun 11 2022 13:52:05
%S 1,1,4,7,14,23,41,63,104,152,230,327,470,647,897,1202,1616,2117,2775,
%T 3566,4580,5787,7301,9092,11298,13885,17028,20688,25076,30154,36172,
%U 43094,51221,60511,71323,83622,97822,113893,132323,153083
%N Number of solid partitions of n supported on graph of cube.
%D P. A. MacMahon, Memoir on the theory of partitions of numbers - Part VI, Phil. Trans. Roal Soc., 211 (1912), 345-373 (see Section 98).
%D 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]
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Matthew House, <a href="/A003404/b003404.txt">Table of n, a(n) for n = 0..10000</a>
%H G. E. Andrews, P. Paule and A. Riese, <a href="http://www.risc.uni-linz.ac.at/research/combinat/risc/publications/#ppaule">MacMahon's partition analysis III. The Omega package</a>, p. 14.
%H G. E. Andrews, P. Paule and A. Riese, <a href="http://dx.doi.org/10.1006/eujc.2001.0527">MacMahon's Partition Analysis: The Omega Package</a>, Europ. J. Combin., 22 (2001), 887-904.
%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, 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).
%F 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)).
%t 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 *)
%t LinearRecurrence[{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},{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},50] (* _Harvey P. Dale_, Jun 11 2022 *)
%Y Cf. A003402, A003403, A003405, A029073, A256975, A256976, A256977.
%K nonn,nice,easy
%O 0,3
%A _N. J. A. Sloane_
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