login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135934 O.g.f.: A(x) = Sum_{n>=0} x^n / Product_{k=0..n} (1 - Fibonacci(k)*x). 1
1, 1, 2, 4, 9, 24, 77, 299, 1419, 8312, 60452, 547939, 6213566, 88468601, 1585646789, 35846274127, 1023893974778, 37005881297226, 1694206791508891, 98335493373334998, 7241161595237290969, 676871453643079089963 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

After the first term, row sums of triangle A111669. - Emanuele Munarini, Dec 05 2017

LINKS

Table of n, a(n) for n=0..21.

FORMULA

G.f.: (1 - G(0) )/(1-x) where G(k) = 1 - 1/(1-Fibonacci(k)*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 17 2013

G.f.: 1/(x*(1-x)*G(0)) - 1/x where G(k) = 1 - x/(x - 1/(1 + 1/(x*Fibonacci(k)-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 13 2013

EXAMPLE

A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-x)) + x^3/((1-x)*(1-x)*(1-2*x)) +

x^4/((1-x)*(1-x)*(1-2*x)(1-3*x)) + x^5/((1-x)*(1-x)*(1-2*x)*(1-3*x)*(1-5*x)) + x^6/((1-x)*(1-x)*(1-2*x)*(1-3*x)*(1-5*x)*(1-8*x)) +...

PROG

(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/prod(j=0, k, 1-fibonacci(j)*x+x*O(x^n))), n)}

CROSSREFS

Cf. A000045, A111669.

Sequence in context: A000667 A131351 A091352 * A210342 A137154 A098448

Adjacent sequences:  A135931 A135932 A135933 * A135935 A135936 A135937

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 07 2007

STATUS

approved

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 October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)