This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007846 #11 Jul 03 2025 17:43:32 %S A007846 1,1,4,24,176,1504,14560,156768,1852512,23783264,329070176,4874845920, %T A007846 76898357216,1285734871520,22695759641440,421508294003424, %U A007846 8211642378316768 %N 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. %C A007846 Description #1 and the extended sequence are from _R. H. Hardin_, 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. %C A007846 Mapping between Descriptions 1 and 3: Renumber 1..n in Description #1 as n..1, so that there is only one local minimum. %D A007846 A. Baram and D. Kutasov, "On the dynamics of random sequential absorption," J. Physics A: Math. Gen. 22, L251-L254 (1989). %D A007846 Y. Fan and J. K. Percus, Use of Model Solutions in RSA on a Lattice, Phys. Rev. Lett. 67, 1677 (1991). %e A007846 Examples for description #1: %e A007846 For n=2 there are 4 possibilities: %e A007846 ................. %e A007846 ..1..2..12..21... %e A007846 ..2..1........... %e A007846 ................. %e A007846 For n=3 there are 24 possibilities: %e A007846 .................... %e A007846 .123..132..231..321. %e A007846 .................... %e A007846 .1..1..2..3......... %e A007846 .2..3..3..2......... %e A007846 .3..2..1..1......... %e A007846 ......................... %e A007846 .12.21..1.32.3...3.1..23. %e A007846 ..3.3..32..1.21.12.23.1.. %e A007846 ......................... %e A007846 .31.13..1.23.2...2.1..32. %e A007846 .2...2.23..1.31.13.32.1.. %e A007846 ......................... %e A007846 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. %Y A007846 If the numbers are constrained to be on a line: A000079, in a square array: A087518, in an n X k array: A087783. %K A007846 nonn,nice %O A007846 0,3 %A A007846 Joel Yellin (yellin(AT)soe.ucsc.edu) %E A007846 New description and more terms from _R. H. Hardin_, Oct 25 2003 %E A007846 Entry revised following comments from Joel Yellin (yellin(AT)soe.ucsc.edu), Mar 04 2004