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 A089299 Number of square plane partitions of n. 13
 1, 1, 1, 1, 2, 2, 4, 5, 8, 11, 16, 21, 31, 41, 57, 78, 108, 146, 202, 274, 375, 509, 690, 929, 1255, 1679, 2246, 2991, 3979, 5266, 6971, 9187, 12104, 15898, 20870, 27322, 35762, 46690, 60927, 79348, 103270, 134138, 174108, 225576, 291990, 377320, 487083 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Number of ways of writing n as a sum p(1,1) + p(1,2) + ... + p(1,k) + p(2,1) + ... + p(2,k) + ... + p(k,1) + ... + p(k,k) for some k so that in the square array {p(i,j)} the numbers are nonincreasing along rows and columns. All the p(i,j) are >= 1. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..4000 FORMULA G.f.: Sum_{k>=0} x^(k^2) / Product_{j=1..2k-1} (1-x^j)^min(j,2k-j). - Franklin T. Adams-Watters, Jun 14 2006 EXAMPLE a(7) = 5: 7 41 32 31 22 . 11 11 21 21 a(10) = 16 from {{10}}, {{3, 2}, {3, 2}}, {{3, 3}, {2, 2}}, {{3, 3}, {3, 1}}, {{4, 1}, {4, 1}}, {{4, 2}, {2, 2}}, {{4, 2}, {3, 1}}, {{4, 3}, {2, 1}}, {{4, 4}, {1, 1}}, {{5, 1}, {3, 1}}, {{5, 2}, {2, 1}}, {{5, 3}, {1, 1}}, {{6, 1}, {2, 1}}, {{6, 2}, {1, 1}}, {{7, 1}, {1, 1}}, {{2, 1, 1}, {1, 1, 1}, {1, 1, 1}}} From Gus Wiseman, Jan 16 2019: (Start) The a(10) = 16 square plane partitions:   [ten] .   [32] [33] [33] [41] [42] [42] [43] [44] [51] [52] [53] [61] [62] [71]   [32] [22] [31] [41] [22] [31] [21] [11] [31] [21] [11] [21] [11] [11] .   [211]   [111]   [111] (End) MATHEMATICA Table[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#, {Length[ptn]}]&/@ptn]], And@@OrderedQ/@Transpose[#]&]], {ptn, IntegerPartitions[n]}], {n, 30}] (* Gus Wiseman, Jan 16 2019 *) CROSSREFS Cf. A008763, A001970, A089292. Cf. A000219, A003293, A101509, A319066, A323429, A323433, A323450. Sequence in context: A241545 A157162 A109434 * A017910 A240734 A328460 Adjacent sequences:  A089296 A089297 A089298 * A089300 A089301 A089302 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 25 2003 EXTENSIONS Corrected and extended by Wouter Meeussen, Dec 30 2003 a(21)-a(25) from John W. Layman, Jan 02 2004 More terms from Franklin T. Adams-Watters, Jun 14 2006 Name edited by Gus Wiseman, Jan 16 2019 STATUS approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)