A309019 Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)) + x^(2^(k+2))).

0, 1, 1, 2, 1, 4, 2, 4, 1, 7, 4, 7, 2, 10, 4, 7, 1, 12, 7, 12, 4, 18, 7, 13, 2, 19, 10, 16, 4, 21, 7, 12, 1, 20, 12, 20, 7, 31, 12, 23, 4, 34, 18, 29, 7, 38, 13, 22, 2, 34, 19, 31, 10, 45, 16, 30, 4, 41, 21, 32, 7, 40, 12, 20, 1, 33, 20, 33, 12, 52, 20, 39, 7, 58, 31, 50, 12, 66, 23, 39, 4, 61, 34, 56, 18, 81, 29, 54, 7, 74, 38

Offset: 0

Author

Ilya Gutkovskiy, Jul 06 2019

Keywords

• nonn

Crossrefs

Cf. A002487, A309020, A309021, A309022.

Programs

Mathematica

nmax = 90; CoefficientList[Series[x Product[(1 + x^(2^k) + x^(2^(k + 1)) + x^(2^(k + 2))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 3)/2] + a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 90}]

Formula

a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-1) + a(n) + a(n+1).