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A029886 Convolution of Thue-Morse sequence A001285 with itself. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

FORMULA

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

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-Fran├žois Alcover, Aug 31 2018 *)

PROG

(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

CROSSREFS

Cf. A001285.

Sequence in context: A310975 A310976 A155878 * A102218 A257586 A172458

Adjacent sequences:  A029883 A029884 A029885 * A029887 A029888 A029889

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 11 16:42 EDT 2021. Contains 342888 sequences. (Running on oeis4.)