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First differences of A019300.
2

%I #12 Feb 13 2022 05:05:40

%S 1,2,3,7,13,26,53,106,211,422,845,1689,3379,6758,13515,27031,54061,

%T 108122,216245,432489,864979,1729958,3459915,6919830,13839661,

%U 27679322,55358643,110717287,221434573,442869146,885738293,1771476586,3542953171

%N First differences of A019300.

%C Partial sums give A019300, while partial sums mod 2 = the Thue-Morse sequence, A010060. a(n) mod 2 = A035263: 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, ...

%F a(n+1) = 2*a(n) + 0 or +-1. - _Robert G. Wilson v_, Sep 27 2003

%F a(n+1) = 2*a(n) + A029883(n). - _Philippe Deléham_, Mar 21 2004

%t tm = Table[ If[ OddQ[ Count[ IntegerDigits[n, 2], 1]], 1, 0], {n, 0, 35}]; Table[ FromDigits[ Take[ tm, n + 1], 2] - FromDigits[ Take[ tm, n], 2], {n, 1, 33}] (* _Robert G. Wilson v_ *)

%Y Cf. A019300, A010060, A035263.

%K nonn

%O 1,2

%A _Gary W. Adamson_, Sep 21 2003

%E More terms from _Robert G. Wilson v_, Sep 27 2003