A029886 Convolution of Thue-Morse sequence A001285 with itself.

1, 4, 8, 10, 12, 14, 15, 16, 22, 24, 23, 26, 29, 30, 34, 40, 38, 40, 43, 42, 47, 50, 52, 56, 55, 56, 62, 66, 64, 70, 71, 64, 78, 80, 75, 82, 83, 82, 88, 96, 89, 92, 100, 98, 102, 106, 105, 104, 111, 112, 114, 122, 118, 122, 125, 120, 130, 136, 131, 130, 141, 134, 138, 160

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Comment from Jeremy Gardiner, Dec 28 2008: The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, There are no coincidences, arXiv preprint 1410.2193 [math.CO], 2014.

Crossrefs

Cf. A001285.

Programs

Mathematica

P[n_, x_] := (bb = IntegerDigits[n, 2]) . x^Range[Length[bb]-1, 0, -1];
TM[n_] := 1 + Mod[P[n, 1], 2];
a[n_] := Sum[TM[k] TM[n-k], {k, 0, n}];
Table[a[n], {n, 0, 63}] (* Jean-François Alcover, Aug 31 2018 *)

PARI

a(n)=sum(k=0,n,(1+subst(Pol(binary(k)),x,1)%2)*(1+subst(Pol(binary(n-k)),x,1)%2)) \\ Ralf Stephan, Aug 23 2013

Formula

G.f.: (1/4)*(3/(1 - x) - Product_{k>=0} (1 - x^(2^k)))^2. - Ilya Gutkovskiy, Apr 03 2019