A180125 Self-convolution of period-doubling sequence A035263.

0, 1, 0, 2, 2, 3, 2, 5, 2, 5, 2, 6, 4, 7, 4, 10, 6, 9, 6, 12, 8, 11, 8, 15, 8, 13, 8, 16, 10, 15, 10, 21, 10, 17, 10, 20, 12, 19, 12, 25, 12, 21, 12, 24, 14, 23, 14, 30, 16, 25, 16, 30, 18, 27, 18, 35, 18, 29, 18, 34, 20, 31, 20, 42, 22, 33, 22, 40, 24, 35, 24, 45, 24, 37

Offset: 1

Author

Jacob A. Siehler, Aug 11 2010

Keywords

• nonn

Comments

Reducing a(n) mod 2 gives 1-A035263(n), which is also A096268(n+1).

Crossrefs

Cf. A035263, A096268

Programs

Mathematica

b[i_] := b[i] = If[OddQ[i], 1, 1 - b[i/2]]; a[n_] := Sum[b[i] b[n - i], {i, 1, n - 1}]

Formula

a(n) = sum(b(i)b(n-i), i=1..(n-1)), where b(i)=A035263(i).