Description #1 and the extended sequence are from _R. H. Hardin (rhhardin(AT)att.net), _, Oct 25 2003. The sequence was originally submitted by Joel Yellin (yellin(AT)soe.ucsc.edu), who referenced the literature on random sequential adsorption (RSA) and used description #3.
New description and more terms from _R. H. Hardin (rhhardin(AT)att.net), _, Oct 25 2003
Description #1 and the extended sequence are from Ron R. H. Hardin (rhhardin(AT)att.net), Oct 25 2003. The sequence was originally submitted by Joel Yellin (yellin(AT)soe.ucsc.edu), who referenced the literature on random sequential adsorption (RSA) and used description #3.
nonn,nice,new
New description and more terms from Ron R. H. Hardin (rhhardin(AT)att.net), Oct 25 2003
Description #1 and the extended sequence are from Ron Hardin (rhhrhhardin(AT)cadenceatt.comnet), Oct 25 2003. The sequence was originally submitted by Joel Yellin (yellin(AT)soe.ucsc.edu), who referenced the literature on random sequential adsorption (RSA) and used description #3.
nonn,nice,new
New description and more terms from Ron Hardin (rhhrhhardin(AT)cadenceatt.comnet), Oct 25 2003
There are three equivalent descriptions: 1. Number of (horizontally or vertically) connected arrays of 1..n on rectangular grid (otherwise zero) with only one local maximum. 2. Number of n-polyominos polyominoes labeled 1...n such that each successive labeled cell is the neighbor of a previously labeled cell. 3. Number of connected n-step paths on a rectangular lattice, diagonal or repeated steps not allowed.
nonn,nice,new
There are three equivalent descriptions: 1. Number of arrangements (horizontally or vertically) connected arrays of 1..n on rectangular grid (otherwise zero) with only one local maximum. 2. Number of n-polyominos labeled 1...n such that each successive labeled cell is the neighbor of a previously labeled cell. 3. Number of connected n-step paths on a rectangular lattice, diagonal or repeated steps not allowed.
Neighbors Description #1 and the extended sequence are considered only in x from Ron Hardin (rhh(AT)cadence.com), Oct 25 2003. The sequence was originally submitted by Joel Yellin (yellin(AT)soe.ucsc.edu), who referenced the literature on random sequential adsorption (RSA) and y directionsused description #3.
Mapping between Descriptions 1 and 3: Renumber 1..n in Description #1 as n..1, so that there is only one local minimum.
Y. Fan and J. K. Percus, Use of Model Solutions in RSA on a Lattice, Phys. Rev. Lett. 67, 1677 (1991).
Examples for description #1:
.2...2.23..1.31.3113.32.1..
Examples for description #3. n=3: Place step #3 on each of six possible nearest neighbor (NN) sites of the 4 n=2 configurations given below for description #1. Total instances = 4 X 6 = 24. n=4: Place step #4 on each of 8 NN sites of 8 (straight line) configurations of the form 123. Place step #4 on each of 7 NN sites of 16 configurations of the form 12/3 (with the 3 under the 1). Total instances = 8 X 8 + 7 X 16 = 176.
nonn,nice,new
Joel Yellin (yellin(AT)csesoe.ucsc.edu)
Better New description and more terms from Ron Hardin (rhh(AT)cadence.com), Oct 25 2003
Entry revised following comments from Joel Yellin (yellin(AT)soe.ucsc.edu), Mar 04, 2004
From random sequential absorption in 2 dimensions under nearest neighbor blockingNumber of arrangements of 1..n on rectangular grid (otherwise zero) with only one local maximum.
1, 1, 4, 24, 176, 1504, 14560, 156768, 1852512, 23783264, 329070176, 4874845920, 76898357216, 1285734871520, 22695759641440, 421508294003424, 8211642378316768
Neighbors are considered only in x and y directions.
For n=2 there are 4 possibilities:
.................
..1..2..12..21...
..2..1...........
.................
For n=3 there are 24 possibilities:
....................
.123..132..231..321.
....................
.1..1..2..3.........
.2..3..3..2.........
.3..2..1..1.........
.........................
.12.21..1.32.3...3.1..23.
..3.3..32..1.21.12.23.1..
.........................
.31.13..1.23.2...2.1..32.
.2...2.23..1.31.31.32.1..
.........................
nonn,newnice
Joel Yellin [ (yellin(AT)cse.ucsc.edu ])
Better description and more terms from Ron Hardin (rhh(AT)cadence.com), Oct 25 2003
From random sequential adsorption absorption in 2 dimensions under nearest neighbor blocking.
nonn,new
nonn
Joel Yellin [ yellin@(AT)cse.ucsc.edu ]
JPA A22 A. Baram and D. Kutasov, "On the dynamics of random sequential absorption," J. Physics A: Math. Gen. 22, L251 89-L254 (1989).
nonn,new
nonn
Joel Yellin [ yellin@cse.ucsc.edu ]
From random sequential adsorption in 2 dimensions under nearest neighbor blocking.
1, 1, 4, 24, 176, 1504, 14560, 156768, 1852512, 23783264, 329070176
0,3
JPA A22 L251 89.
nonn
Joel Yellin [yellin@cse.ucsc.edu]
approved