login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A303666 Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))). 1

%I

%S 1,2,4,7,13,23,41,72,128,226,400,706,1248,2204,3894,6877,12149,21459,

%T 37907,66957,118275,208919,369037,651863,1151453,2033921,3592719,

%U 6346167,11209863,19801075,34976589,61782572,109132628,192771658,340511506,601478868,1062451154,1876711698,3315020026

%N Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))).

%C Partial sums of A023359.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%p b:= proc(n) option remember;

%p `if`(n=0, 1, add(b(n-2^i), i=0..ilog2(n)))

%p end:

%p a:= proc(n) option remember;

%p `if`(n<0, 0, b(n)+a(n-1))

%p end:

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 28 2018

%t nmax = 38; CoefficientList[Series[1/((1 - x) (1 - Sum[x^2^k, {k, 0, nmax}])), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = Sum[Boole[k == 2^IntegerExponent[k, 2]] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 38}]]

%Y Cf. A000079, A000123, A023359, A209229.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 28 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)