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A144026 An INVERT transform of the Thue-Morse sequence. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)