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A096272
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Triangle read by rows: T[n,k] counts solid partitions of n such that the maximum of planes, rows, columns and values is k.
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10
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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; internal format)
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OFFSET
| 1,3
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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, ...
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LINKS
| Wouter Meeussen, SolidPartitions.txt
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EXAMPLE
| {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 not more than 2 columns, each column no more than 2 rows and each element is no larger than 2.
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MATHEMATICA
| Max[ Max @(Flatten@(List @@ #)), Max @@ Map[Length, #, {-2}], Length /@ List @@ #, Length[ # ]] & /@ Flatten[solidformBTK /@ Partitions[n]]]], {n, 12}]; (* see link for function definition *)
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CROSSREFS
| Cf. A094508, A007760, A094504, A000293.
Sequence in context: A010637 A200692 A127447 * A021715 A075443 A021250
Adjacent sequences: A096269 A096270 A096271 * A096273 A096274 A096275
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KEYWORD
| nonn,tabl
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 22 2004, Sep 21 2008
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