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A047913
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Triangle of numbers a(n,k) = no of partitions of k such that k=n+n_1+n_2+...+n_t where n_1<=2n and n_{i+1}<=2n_i for all i.
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6
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1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 4, 7, 9, 1, 1, 2, 4, 7, 12, 16, 1, 1, 2, 4, 7, 13, 22, 28, 1, 1, 2, 4, 7, 13, 24, 39, 50, 1, 1, 2, 4, 7, 13, 24, 42, 70, 89, 1, 1, 2, 4, 7, 13, 24, 43, 76, 126, 159, 1, 1, 2, 4, 7, 13, 24, 43, 78, 137, 225, 285
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Triangle is read in this order: a(1,1), a(2,2), a(1,2), a(3,3), a(2,3), a(1,3), a(4,4), ...
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REFERENCES
| Minc, H.; A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
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FORMULA
| a(n, n)=1, a(n, k)=Sum_{i=1..2n} a(i, k-n).
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EXAMPLE
| 1; 1 1; 1 1 2; 1 1 2 3; 1 1 2 4 5; ...
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CROSSREFS
| Rows give A002572, A002573, A002574, ..., columns approach A002843. Cf. A049286 for another version.
Sequence in context: A180562 A199711 A048887 * A152977 A117935 A179749
Adjacent sequences: A047910 A047911 A047912 * A047914 A047915 A047916
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KEYWORD
| tabl,nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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