|
Search: id:A007846
|
|
|
| A007846 |
|
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-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. |
|
+0
13
|
|
| 1, 1, 4, 24, 176, 1504, 14560, 156768, 1852512, 23783264, 329070176, 4874845920, 76898357216, 1285734871520, 22695759641440, 421508294003424, 8211642378316768
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Description #1 and the extended sequence are from Ron 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.
Mapping between Descriptions 1 and 3: Renumber 1..n in Description #1 as n..1, so that there is only one local minimum.
|
|
REFERENCES
|
A. Baram and D. Kutasov, "On the dynamics of random sequential absorption," J. Physics A: Math. Gen. 22, L251-L254 (1989).
Y. Fan and J. K. Percus, Use of Model Solutions in RSA on a Lattice, Phys. Rev. Lett. 67, 1677 (1991).
|
|
EXAMPLE
|
Examples for description #1:
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..1.31.13.32.1..
.........................
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.
|
|
CROSSREFS
|
If the numbers are constrained to be on a line: A000079, in a square array: A087518, in an n X k array: A087783.
Sequence in context: A156017 A000309 A112914 this_sequence A139702 A061720 A152403
Adjacent sequences: A007843 A007844 A007845 this_sequence A007847 A007848 A007849
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
Joel Yellin (yellin(AT)soe.ucsc.edu)
|
|
EXTENSIONS
|
New description and more terms from Ron Hardin (rhhardin(AT)att.net), Oct 25 2003
Entry revised following comments from Joel Yellin (yellin(AT)soe.ucsc.edu), Mar 04, 2004
|
|
|
Search completed in 0.002 seconds
|
