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A048600
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Triangle a(n,k) = number of colors that can be produced by n units of paint from k primary colors.
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0
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1, 1, 2, 1, 3, 3, 1, 5, 6, 4, 1, 7, 13, 10, 5, 1, 11, 22, 26, 15, 6, 1, 13, 40, 51, 45, 21, 7, 1, 19, 55, 103, 100, 71, 28, 8, 1, 23, 88, 161, 221, 176, 105, 36, 9, 1, 29, 118, 277, 386, 422, 287, 148, 45, 10
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| All partitions of size n: if GCD is not 1, skip; else: fill the partition with zeros to get k numbers; count occurrences of each number (e.g.: 2 2 1 0 0 0 becomes 2 1 3); compute multinomial of k over these digits (e.g. 2 1 3 becomes 6!/(2!*1!*3!) = 60; sum.
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EXAMPLE
| Table read by antidiagonals: (1), (1 2), (1 3 3), (1 5 6 4), (1 7 13 10 5), ...
a(2,3)=6 because you can take each color once, or mix two colors.
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CROSSREFS
| Row 2 = A005728, row 3 = A048134. Cf. A048240, A048241.
Sequence in context: A180165 A142249 A097351 * A100578 A061315 A144265
Adjacent sequences: A048597 A048598 A048599 * A048601 A048602 A048603
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KEYWORD
| easy,nice,nonn,tabl
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AUTHOR
| Jurjen N.E. Bos (J.Bos at Interpay-ISS dot demon dot nl)
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