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A308558
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Triangle read by rows where T(n,k) is the number of integer partitions of n > 0 into powers of k > 0.
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1
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1, 1, 2, 1, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 2, 1, 6, 3, 2, 2, 2, 1, 6, 3, 2, 2, 2, 2, 1, 10, 3, 3, 2, 2, 2, 2, 1, 10, 5, 3, 2, 2, 2, 2, 2, 1, 14, 5, 3, 3, 2, 2, 2, 2, 2, 1, 14, 5, 3, 3, 2, 2, 2, 2, 2, 2, 1, 20, 7, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 20, 7, 4, 3, 3, 2
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Triangle begins:
1
1 2
1 2 2
1 4 2 2
1 4 2 2 2
1 6 3 2 2 2
1 6 3 2 2 2 2
1 10 3 3 2 2 2 2
1 10 5 3 2 2 2 2 2
1 14 5 3 3 2 2 2 2 2
1 14 5 3 3 2 2 2 2 2 2
1 20 7 4 3 3 2 2 2 2 2 2
1 20 7 4 3 3 2 2 2 2 2 2 2
Row n = 6 counts the following partitions:
(111111) (42) (33) (411) (51) (6)
(222) (3111) (111111) (111111) (111111)
(411) (111111)
(2211)
(21111)
(111111)
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MATHEMATICA
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Table[If[k==1, 1, Length[Select[IntegerPartitions[n], And@@(IntegerQ[Log[k, #]]&/@#)&]]], {n, 10}, {k, n}]
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CROSSREFS
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Same as A102430 except for the k = 1 column.
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KEYWORD
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AUTHOR
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STATUS
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approved
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