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 A096272 Triangle read by rows: T(n,k) counts solid partitions of n such that the maximum of planes, rows, columns and values is k. 10
 1, 0, 4, 0, 6, 4, 0, 10, 12, 4, 0, 13, 30, 12, 4, 0, 18, 70, 36, 12, 4, 0, 19, 142, 94, 36, 12, 4, 0, 24, 274, 234, 100, 36, 12, 4, 0, 19, 501, 534, 258, 100, 36, 12, 4, 0, 18, 872, 1186, 630, 264, 100, 36, 12, 4, 0, 13, 1449, 2486, 1482, 654, 264, 100, 36, 12, 4, 0, 10, 2336 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Solid partitions of n that fit inside a 4-dimensional k X k X k X k box. Regard solid partitions as safe pilings of boxes in a corner, stacking height does not increase away from the corner and each box contains an integer and this integer too does not increase away from the corner. If k > 1+(n/2) then T(n,k) = T(n-1,k-1). For large n and k, each row ends as the reverse of 4, 12, 36, 100, 264, 660, 1608, 3772, 8652, 19340, 42392, 91140, 192860, 401880, 836480, ... = 4*A096322(i), i>=1. LINKS Wouter Meeussen, SolidPartitions.txt EXAMPLE Triangle T(n,k) begins: 1; 0,  4; 0,  6,  4; 0, 10, 12,  4; 0, 13, 30, 12,  4; 0, 18, 70, 36, 12, 4; ... T(16,2) = 1 because only { {{2,2},{2,2}}, {{2,2},{2,2}} } has only two planes, each plane has no more than 2 columns, each column no more than 2 rows and each element is no larger than 2. MATHEMATICA Max[ Max @(Flatten@(List @@ #)), Max @@ Map[Length, #, {-2}], Length /@ List @@ #, Length[ # ]] & /@ Flatten[solidformBTK /@ Partitions[n]]]], {n, 12}]; (* see link for function definition *) CROSSREFS Cf. A000293, A007760, A094504, A094508, A096322. Sequence in context: A226775 A305731 A279433 * A021715 A327278 A278210 Adjacent sequences:  A096269 A096270 A096271 * A096273 A096274 A096275 KEYWORD nonn,tabl AUTHOR Wouter Meeussen, Jun 22 2004, Sep 21 2008 STATUS approved

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Last modified January 21 16:54 EST 2020. Contains 331114 sequences. (Running on oeis4.)