login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162891 Expansion of 1 / Product_{k>=1} (1-x^k-x^(2*k)). 10
1, 1, 3, 5, 11, 18, 36, 59, 109, 181, 318, 525, 902, 1481, 2492, 4087, 6788, 11090, 18274, 29776, 48772, 79332, 129411, 210172, 341958, 554728, 900872, 1460298, 2368555, 3837147, 6218652, 10070389, 16311432, 26407350, 42757335, 69208746, 112032256, 181316714 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ p / (sqrt(5) * r^(n+1)), where r = (sqrt(5)-1)/2 and p = Product_{n>1} 1/(1 - r^n - r^(2*n)) = 4.64451592505133910330213147... . - Vaclav Kotesovec, Nov 16 2016

MAPLE

F:= n-> combinat[fibonacci](n+1):

b:= proc(n, i) option remember; `if`(n=0 or i=1, F(n),

add((t-> b(t, min(t, i-1)))(n-i*j)*F(j), j=0..n/i))

end:

a:= n-> b(n$2):

seq(a(n), n=0..39); # Alois P. Heinz, Aug 24 2019

MATHEMATICA

nmax = 50; CoefficientList[Series[1/Product[1-x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 16 2016 *)

PROG

(PARI) al(n)=Vec(1/prod(k=1, n, 1-x^k-x^(2*k)+x*O(x^n)))

(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(1/(&*[(1-x^k-x^(2*k)): k in [1..100]]))); // G. C. Greubel, Oct 24 2018

CROSSREFS

Cf. A000045, A000041, A001156, A003105, A263401, A276527.

Sequence in context: A281357 A320789 A269628 * A320351 A319641 A306895

Adjacent sequences: A162888 A162889 A162890 * A162892 A162893 A162894

KEYWORD

nonn,easy

AUTHOR

Franklin T. Adams-Watters, Jul 16 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)