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A089052
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Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) = number of partitions of n into exactly k powers of 2.
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5
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1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 1, 2, 2, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 3, 3, 2, 2, 2, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,25
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FORMULA
| T(2m, k) = T(m, k)+T(2m-1, k-1); T(2m+1, k) = T(2m, k-1).
G.f.: 1/Product_{k>=0} (1-y*x^(2^k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 03 2003
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MAPLE
| T := proc(n, k) option remember; if k > n then RETURN(0); fi; if k= 0 then if n=0 then RETURN(1) else RETURN(0); fi; fi; if n mod 2 = 1 then RETURN(T(n-1, k-1)); fi; T(n-1, k-1)+T(n/2, k); end;
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CROSSREFS
| Columns give A036987, A075897 (essentially), A089049, A089050, A089051, row sums give A018819. See A089053 for another version.
Sequence in context: A176724 A015318 A026836 * A142475 A051556 A081602
Adjacent sequences: A089049 A089050 A089051 * A089053 A089054 A089055
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2003
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