The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A079216 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A079216

Square array A(n>=0,k>=1) (listed antidiagonally: A(0,1)=1, A(1,1)=1, A(0,2)=1, A(2,1)=2, A(1,2)=1, A(0,3)=1, A(3,1)=3, ...) giving the number of n-edge general plane trees fixed by k-fold application of Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).
(history; published version)

#12 by Russ Cox at Sat Mar 31 13:21:09 EDT 2012

AUTHOR

_Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com) _ Jan 03 2002

Discussion

Sat Mar 31

13:21

OEIS Server: https://oeis.org/edit/global/881

#11 by Russ Cox at Sun Jul 10 18:40:55 EDT 2011

LINKS

<a href="/Sindx_index/Par.html#parens">Index entries for sequences related to parenthesizing</a>

Discussion

Sun Jul 10

18:40

OEIS Server: https://oeis.org/edit/global/63

#10 by Joerg Arndt at Sun Jun 05 05:35:35 EDT 2011

STATUS

reviewed

approved

#9 by Antti Karttunen at Sat Jun 04 17:03:44 EDT 2011

STATUS

proposed

reviewed

#8 by Antti Karttunen at Sat Jun 04 17:02:54 EDT 2011

NAME

Square array A(n>=0,k>=1) (listed antidiagonally: A(0,1)=1, A(1,1)=1, A(0,2)=1, A(2,1)=2, A(1,2)=1, A(0,3)=1, A(3,1)=3, ...) giving the number of n-edge general plane trees fixed by k-fold application of the gatomorphisms Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).

LINKS

A. Karttunen, <a href="http://www.ikioeis.fi/~kartturi/matikkaorg/Nekomorphismswiki/gatomorf.htmCatalan_Automorphisms">GatomorphismsCatalan Automorphisms</a>

AUTHOR

Antti Karttunen (my_firstnameHis-Firstname.my_surnameHis-Surname(AT)gmail.com) Jan 03 2002

STATUS

approved

proposed

Discussion

Sat Jun 04

17:03

Antti Karttunen: A part of general "gatomorphism" -> "Catalan automorphism" clean-up. Changed my link to a more maintainable OEIS-Wiki page.

#7 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_Par.html#parens">Index entries for sequences related to parenthesizing</a>

KEYWORD

nonn,tabl,new

#6 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

LINKS

A. Karttunen, <A HREFa href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</Aa>

<a href="http://www.research.att.com/~njas/sequences/Sindx_Par.html#parens">Index entries for sequences related to parenthesizing</a>

KEYWORD

nonn,tabl,new

#5 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

KEYWORD

nonn,tabl,new

AUTHOR

Antti Karttunen (my_firstname.my_surname(AT)ikigmail.ficom) Jan 03 2002

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

FORMULA

A(0, k) = 1. A(n, k) = Sum_{r=1..n where r/gcd(r, k) divides n} Sum_{c as each composition of n/(r/gcd(r, k)) into gcd(r, k) parts} Product_{i as each composant of c} A(i-1, lcm(r, k))

KEYWORD

nonn,tabl,new

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

MAPLE

[seq(A079216(n), n=0..119)]; A079216 := n -> A079216bi(A025581(n), A002262(n)+1);

KEYWORD

nonn,tabl,new