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A072170
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Square array T(n,k) (n >= 0, k >= 2) read by antidiagonals, where T(n,k) is the number of ways of writing n as Sum_{i=0..inf} c_i 2^i, c_i in {0,1,...,k-1}.
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7
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 3, 3, 4, 2, 2, 1, 1, 1, 1, 4, 3, 4, 2, 2, 1, 1, 1, 4, 4, 5, 4, 4, 2, 2, 1, 1, 1, 3, 5, 4, 5, 4, 4, 2, 2, 1, 1, 1, 5, 6, 8, 5, 6, 4, 4, 2, 2, 1, 1, 1, 2, 6, 6, 8, 5, 6, 4, 4, 2, 2, 1, 1, 1, 5, 6, 9, 8, 9, 6, 6
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| k-th column is k-th binary partition function.
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REFERENCES
| B. Reznick, Some binary partition functions, in "Analytic number theory" (Conf. in honor P. T. Bateman, Allerton Park, IL, 1989), 451-477, Progr. Math., 85, Birkhaeuser Boston, Boston, MA, 1990.
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EXAMPLE
| Array begins:
1 1 1 1 1 1 1 1 ...
1 1 1 1 1 1 1 1 ...
1 2 2 2 2 2 2 2 ...
1 1 2 2 2 2 2 2 ...
1 2 3 3 4 4 4 4 ...
1 3 4 5 5 6 6 6 ...
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CROSSREFS
| k=3 column is A002487, k=4 is integers doubled up, k=5, 6, 7 are A007728, A007729, A007730, limiting (infinity) column is A000123 doubled up.
Sequence in context: A151683 A133912 A122934 * A056624 A193348 A093997
Adjacent sequences: A072167 A072168 A072169 * A072171 A072172 A072173
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 29 2002
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