The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A130136

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A130136

Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 0110's (n>=0, 0<=k<=floor((n-1)/3)). A Fibonacci binary word is a binary word having no 00 subword.
(history; published version)

#11 by Peter Luschny at Wed Aug 25 06:59:09 EDT 2021

STATUS

reviewed

approved

#10 by Joerg Arndt at Wed Aug 25 05:35:05 EDT 2021

STATUS

proposed

reviewed

#9 by Jon E. Schoenfield at Wed Aug 25 05:34:47 EDT 2021

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Wed Aug 25 05:34:44 EDT 2021

EXAMPLE

1;

2;

3;

5;

7, 1;

11, 2;

16, 5;

25, 8, 1;

STATUS

proposed

editing

#7 by Michel Marcus at Wed Aug 25 02:48:18 EDT 2021

STATUS

editing

proposed

#6 by Michel Marcus at Wed Aug 25 02:48:11 EDT 2021

COMMENTS

Row n has 1+floor((n-1)/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=A130137(n). Sum(k*T(n,k), k>=0)=A001629(n-2) (n>=2).

FORMULA

T(n,0) = A130137(n).

Sum_{k>=0} k*T(n,k) = A001629(n-2) (n>=2).

#5 by Michel Marcus at Wed Aug 25 02:46:33 EDT 2021

FORMULA

G.f.=: G(t,z) =[ (1+z+(1-t)z^3])/[(1-z-z^2+(1-t)z^3-(1-t)z^4]).

EXAMPLE

1;

2;

3;

5;

7,1;

11,2;

16,5;

25,8,1;

...

STATUS

proposed

editing

#4 by Jean-François Alcover at Wed Aug 25 02:33:35 EDT 2021

STATUS

editing

proposed

#3 by Jean-François Alcover at Wed Aug 25 02:33:29 EDT 2021

MATHEMATICA

gf = (1 + z + (1-t) z^3)/(1 - z - z^2 + (1-t) z^3 - (1-t) z^4);

CoefficientList[#, t]& /@ CoefficientList[gf + O[z]^20, z] // Flatten (* Jean-François Alcover, Aug 25 2021 *)

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:36:14 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, May 13 2007

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173