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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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13
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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;
text;
internal format)
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OFFSET
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0,25
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REFERENCES
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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
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LINKS
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FORMULA
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T(2m, k) = T(m, k)+T(2m-1, k-1); T(2m+1, k) = T(2m, k-1).
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EXAMPLE
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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
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MAPLE
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option remember;
if k > n then
return(0);
end if;
if k= 0 then
if n=0 then
return(1)
else
return(0);
end if;
end if;
if n mod 2 = 1 then
return procname(n-1, k-1);
end if;
procname(n-1, k-1)+procname(n/2, k);
end proc:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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