A089053 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = number of partitions of n into exactly k powers of 2.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Dec 03 2003

Keywords

• nonn
• tabl

Crossrefs

See A089052, which is the main entry for this triangle.

Programs

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, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)