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Search: id:A102430
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| A102430 |
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Table T(n,k) read by antidiagonals: number of partitions of n into powers of k. |
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+0
5
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| 1, 3, 1, 10, 2, 1, 35, 2, 1, 1, 126, 4, 2, 1, 1, 462, 4, 2, 1, 1, 1, 1716, 6, 2, 2, 1, 1, 1, 6435, 6, 3, 2, 1, 1, 1, 1, 24310, 10, 3, 2, 2, 1, 1, 1, 1, 92378, 10, 3, 2, 2, 1, 1, 1, 1, 1, 352716, 14, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1352078, 14, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 5200300, 20, 5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 20058300, 20, 7, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,2
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COMMENT
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Column 1 is A001700, Column 2 is A018819, Column 3 is A062051. Columns 2..5 are the Molien series A008645, A008650, A008652, A008648. All entries above main diagonal are = 1.
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FORMULA
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T(1, k) = 1, T(n, 1) = choose(2n-1, n), T(n>1, k>1) = T(n-1, k) + (T(n/k, k) if k divides n, else 0)
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EXAMPLE
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T(9,3)=5 partitions of 9 into powers of 3: 111111111, 1111113, 11133, 333, 9
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CROSSREFS
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Cf. A102431, A102432, A102433, A102434, A001700, A018819, A062051, A008645, A008650, A008652, A008648.
Sequence in context: A019427 A008299 A016478 this_sequence A135573 A126953 A134284
Adjacent sequences: A102427 A102428 A102429 this_sequence A102431 A102432 A102433
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Jan 08 2005
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