A019302 Binomial transform of Thue-Morse sequence A010060.

0, 1, 3, 6, 11, 20, 36, 64, 115, 216, 430, 892, 1872, 3888, 7920, 15840, 31315, 61744, 122418, 245348, 497650, 1019032, 2096680, 4312224, 8826320, 17925376, 36070128, 71915616, 142239056, 279671360, 548106816, 1073741824, 2108053075

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{k=0..n} A010060(k) * A007318(n,k). - Reinhard Zumkeller, May 07 2014

G.f.: (1/2)*(1/(1 - 2*x) - (1/(1 - x))*Product_{k>=0} (1 - x^(2^k)/(1 - x)^(2^k))). - Ilya Gutkovskiy, Aug 20 2018

Mathematica

tm[0] = 0;
tm[n_?EvenQ] := tm[n] = tm[n/2]; tm[n_] := tm[n] = 1-tm[(n-1)/2];
a[n_] := Sum[tm[k]*Binomial[n, k], {k, 0, n}];
Table[a[n], {n, 0, 40}]
(* or (since 2015): *)
a[n_] := Sum[ThueMorse[k]*Binomial[n, k], {k, 0, n}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 30 2015, updated Jul 19 2022 *)

Prog

(Haskell)
a019302 = sum . zipWith (*) a010060_list . a007318_row
-- Reinhard Zumkeller, May 07 2014

Crossrefs

Cf. A007318, A010060.

Sequence in context: A018918 A077855 A054887 * A119861 A255061 A018075

Adjacent sequences: A019299 A019300 A019301 * A019303 A019304 A019305

Keyword

nonn,nice

Author

Jonas Wallgren

Extensions

More terms from Carl Najafi, Sep 08 2011

Status

approved