The On-Line Encyclopedia of Integer Sequences (OEIS)

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A062750

Generalized Catalan array FS(4; n,r).
(history; published version)

#11 by Susanna Cuyler at Tue Oct 30 20:18:01 EDT 2018

STATUS

proposed

approved

#10 by Michel Marcus at Tue Oct 30 12:53:03 EDT 2018

STATUS

editing

proposed

#9 by Michel Marcus at Tue Oct 30 12:53:00 EDT 2018

REFERENCES

D.D. Frey, J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

LINKS

D. D. Frey and J. A. Sellers, <a href="http://www.fq.math.ca/Scanned/39-2/frey.pdf">Generalizing Bailey's generalization of the Catalan numbers</a>, The Fibonacci Quarterly, 39 (2001) 142-148.

STATUS

approved

editing

#8 by Russ Cox at Sat Mar 31 13:20:06 EDT 2012

AUTHOR

_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), _, Jul 12 2001

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/878

#7 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

a(0, 0)=1, a(n, -1)=0, n >= 1; a(n, r)=0 if r>3*n; a(n, r)=a(n, r-1)+a(n-1, r) else.

G.f. for column r=3*k+j, k >= 0, j=1, 2, 3: (x^(k+1))*N(4; k, x)/(1-x)^(3*k+1+j), with the row polynomials N(4; k, x) of array A062751.

KEYWORD

nonn,easy,tabf,new

#6 by N. J. A. Sloane at Sat Apr 09 03:00:00 EDT 2005

COMMENTS

The step width sequence of this tabf staircase array is [1,3,3,3,....], i.e. the degree of the row polynomials is [0,3,6,9,...]= A008585.

KEYWORD

nonn,easy,tabf,new

#5 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

REFERENCES

D.D. Frey, J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

KEYWORD

nonn,easy,tabf,new

#4 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

COMMENTS

The columns r=0..6 give A000012 (powers of 1), A000027 (natural), A000217 (triangular), A000292 (tetrahedral), A063258, A027659, A062966.

KEYWORD

nonn,easy,tabf,new

#3 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

NAME

Generalized Catalan array FS(4; n,r).

COMMENTS

In the Frey-Sellers ref. reference this array is called {n over r}_{m-1}, with m=4.

FORMULA

G.f. for column r=3*k+j, k >= 0, j=1,2,3: (x^(k+1))*N(4; k,x)/(1-x)^(3*k+1+j), with the row polynomials N(4; k,x) of array A062751.

EXAMPLE

{1}; {1,1,1,1}; {1,2,3,4,4,4,4}; {1,3,6,10,14,18,22,22,22,22}; ...; N(4; 1,x)=(2-x)*(2-2*x+x^2).

KEYWORD

nonn,easy,tabf,new

#2 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

EXAMPLE

{1};{1,1,1,1};{1,2,3,4,4,4,4};{1,3,6,10,14,18,22,22,22,22}; ...; N(4;1,x)=(2-x)*(2-2*x+x^2).

KEYWORD

nonn,easy,tabf,new