A296834 - OEIS

%I #4 Dec 21 2017 12:45:32

%S 2,3,3,5,6,5,8,14,14,8,13,31,43,31,13,21,70,132,132,70,21,34,157,402,

%T 573,402,157,34,55,353,1230,2441,2441,1230,353,55,89,793,3755,10485,

%U 14379,10485,3755,793,89,144,1782,11475,44951,85500,85500,44951,11475,1782,144

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.

%C Table starts

%C ..2....3.....5......8.......13........21.........34...........55............89

%C ..3....6....14.....31.......70.......157........353..........793..........1782

%C ..5...14....43....132......402......1230.......3755........11475.........35054

%C ..8...31...132....573.....2441.....10485......44951.......192730........826498

%C .13...70...402...2441....14379.....85500.....508111......3017667......17931240

%C .21..157..1230..10485....85500....706534....5834429.....48122349.....397252886

%C .34..353..3755..44951...508111...5834429...67007971....768117235....8815633972

%C .55..793.11475.192730..3017667..48122349..768117235..12228697715..194991656916

%C .89.1782.35054.826498.17931240.397252886.8815633972.194991656916.4321362259224

%H R. H. Hardin, <a href="/A296834/b296834.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3)

%F k=3: [order 15]

%F k=4: [order 50]

%e Some solutions for n=5 k=4

%e ..0..0..1..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1

%e ..1..0..1..1. .1..1..1..1. .0..0..1..0. .0..0..0..0. .0..1..0..0

%e ..0..0..0..0. .1..1..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0

%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..1. .0..1..0..0

%e ..0..0..1..0. .0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..1

%Y Column 1 is A000045(n+2).

%Y Column 2 is A006356.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 21 2017