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 A089052 Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) = number of partitions of n into exactly k powers of 2. 7
 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; text; internal format)
 OFFSET 0,25 REFERENCES J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013 LINKS Alois P. Heinz, Rows n = 0..200, flattened J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013 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, Dec 03 2003 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; MATHEMATICA t[n_, k_] := t[n, k] = Which[k > n, 0, k == 0, If[n == 0, 1, 0], Mod[n, 2] == 1, t[n-1, k-1], True, t[n-1, k-1] + t[n/2, k]]; Table[t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014, after Maple *) CROSSREFS Columns give A036987, A075897 (essentially), A089049, A089050, A089051, A319922. Row sums give A018819. See A089053 for another version. Sequence in context: A176724 A015318 A026836 * A284606 A284019 A286135 Adjacent sequences:  A089049 A089050 A089051 * A089053 A089054 A089055 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Dec 03 2003 STATUS approved

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Last modified May 19 22:56 EDT 2019. Contains 323411 sequences. (Running on oeis4.)