[go: up one dir, main page]

login
Revision History for A001854 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Total height of all rooted trees on n labeled nodes.
(history; published version)
#47 by N. J. A. Sloane at Tue Jun 21 19:56:06 EDT 2022
STATUS

editing

approved

#46 by N. J. A. Sloane at Tue Jun 21 19:56:04 EDT 2022
FORMULA

A000435(n)/a(n) ~ 1/2 (see A000435 and the Renyi-Szekeres result mentioned in the Comments). - _David desJardins, _, Jan 20 2017

STATUS

approved

editing

#45 by N. J. A. Sloane at Tue Jun 21 19:55:30 EDT 2022
STATUS

editing

approved

#44 by N. J. A. Sloane at Tue Jun 21 19:55:28 EDT 2022
COMMENTS

Theorem [Renyi-Szekeres, (4,7)]. The average height if the tree is chosen at random is sqrt(2*n*Pi). - _David desJardins, _, Jan 20 2017

STATUS

approved

editing

#43 by Susanna Cuyler at Sun Jun 24 18:29:49 EDT 2018
STATUS

proposed

approved

#42 by Jon E. Schoenfield at Sun Jun 24 15:50:46 EDT 2018
STATUS

editing

proposed

#41 by Jon E. Schoenfield at Sun Jun 24 15:50:44 EDT 2018
NAME

Total height of all rooted trees on n labeled nodes.

COMMENTS

Theorem [Renyi-Szekeres, (4,7)]. The average height if the tree is chosen at random is sqrt(2*n*piPi). - David desJardins, Jan 20 2017.

FORMULA

A000435(n)/a(n) ~ 1/2 (see A000435 and the Renyi-Szekeres result mentioned in the Comments). - David desJardins, Jan 20 2017.

AUTHOR
STATUS

approved

editing

#40 by Susanna Cuyler at Fri Feb 09 21:46:14 EST 2018
STATUS

proposed

approved

#39 by Rachel Barnett at Fri Feb 09 19:33:22 EST 2018
STATUS

editing

proposed

#38 by Rachel Barnett at Fri Feb 09 19:33:17 EST 2018
LINKS

J. Riordan, <a href="/A007401/a007401_8.pdf">The enumeration of trees by height and diameter</a>, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)

STATUS

approved

editing