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%I #6 Mar 07 2021 17:52:34
%S 1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,0,1,2,1,1,1,0,0,1,2,1,1,1,1,1,1,2,2,1,
%T 1,1,0,1,1,1,2,2,1,1,1,0,1,2,2,2,2,2,1,1,1,0,0,1,2,2,2,2,2,1,1,1,0,1,
%U 2,2,3,3,2,2,2,1,1,1,0,0,1,2,2,3,3,2,2,2,1,1,1,0,0,1,3,3,3,4,3,2,2,2,1,1,1
%N Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = number of partitions of n into exactly k powers of 2.
%t 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]];
%t Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Mar 07 2021 *)
%Y See A089052, which is the main entry for this triangle.
%K nonn,tabl
%O 0,18
%A _N. J. A. Sloane_, Dec 03 2003