A144026 An INVERT transform of the Thue-Morse sequence.

1, 1, 2, 3, 6, 10, 18, 32, 58, 103, 184, 329, 588, 1051, 1878, 3357, 6000, 10723, 19164, 34251, 61214, 109404, 195530, 349458, 624562, 1116237, 1994974, 3565481, 6372340, 11388848, 20354510, 36378224, 65016314, 116199213, 207674912, 371163175

Offset

0,3

Comments

Eigensequence for sequence array of A010060(n+1). - Paul Barry, Nov 03 2010

Starting with offset 1 represents the numbers of ordered compositions of n using the odious numbers: (1, 2, 4, 7, 8, 11, ...). Cf. A000069. - Gary W. Adamson, Apr 04 2013

Links

Table of n, a(n) for n=0..35.

Formula

G.f.: 1/(1-(1/2)*(1/(1-x) - (Product_{k>=0} (1-x^(2^k))))). - Paul Barry, Nov 03 2010

a(n) = Sum_{k=0..n-1} A010060(n-k)*a(k) with a(0) = 1. - Johannes W. Meijer, Jun 19 2012

Example

a(4) = A010060(4)*a(0) + A010060(3)*a(1) + A010060(2)*a(2) + A010060(1)*a(3) = (1, 0, 1, 1) dot (1, 1, 2, 3) = 1 + 0 + 2 + 3 = 6.

Maple

A010060:=proc(n) local n2: n2:=convert(n, base, 2): sum(n2[j], j=1..nops(n2)) mod 2; end: a:=proc(n) option remember: if n=0 then 1 else a(n) := add(A010060(n-k)*a(k), k=0..n-1) fi: end: seq(a(n), n=0..34); # Johannes W. Meijer, Jun 19 2012

Prog

(PARI) a(n)=polcoeff(1/(1-sum(i=1, n, (hammingweight(i)%2)*x^i)+O(x^(n+1))), n) \\ Ralf Stephan, Dec 10 2013

Crossrefs

Cf. A010060, A144027.

Cf. A000069.

Sequence in context: A181649 A052972 A018166 * A054152 A240802 A339808

Adjacent sequences: A144023 A144024 A144025 * A144027 A144028 A144029

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 07 2008

Extensions

Edited by Johannes W. Meijer, Jun 19 2012

Status

approved