OFFSET
0,3
COMMENTS
Sum of all parts of all compositions (ordered partitions) of n into powers of 2.
FORMULA
a(n) = n*A023359(n).
MATHEMATICA
nmax = 35; CoefficientList[Series[x D[1/(1 - Sum[x^2^k, {k, 0, Floor[Log[nmax]/Log[2]] + 1}]), x], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Boole[k == 2^IntegerExponent[k, 2]] a[n - k], {k, 1, n}]; Table[n a[n], {n, 0, 35}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 20 2018
STATUS
approved