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

1,4

Comments

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

Links

Table of n, a(n) for n=1..74.

Formula

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

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}]

Crossrefs

Cf. A035263, A096268

Sequence in context: A073023 A378772 A173754 * A342086 A272209 A326842

Adjacent sequences: A180122 A180123 A180124 * A180126 A180127 A180128

Keyword

nonn

Author

Jacob A. Siehler, Aug 11 2010

Status

approved