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A296834 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.

%I A296834 #4 Dec 21 2017 12:45:32
%S A296834 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 A296834 573,402,157,34,55,353,1230,2441,2441,1230,353,55,89,793,3755,10485,
%U A296834 14379,10485,3755,793,89,144,1782,11475,44951,85500,85500,44951,11475,1782,144
%N A296834 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.
%C A296834 Table starts
%C A296834 ..2....3.....5......8.......13........21.........34...........55............89
%C A296834 ..3....6....14.....31.......70.......157........353..........793..........1782
%C A296834 ..5...14....43....132......402......1230.......3755........11475.........35054
%C A296834 ..8...31...132....573.....2441.....10485......44951.......192730........826498
%C A296834 .13...70...402...2441....14379.....85500.....508111......3017667......17931240
%C A296834 .21..157..1230..10485....85500....706534....5834429.....48122349.....397252886
%C A296834 .34..353..3755..44951...508111...5834429...67007971....768117235....8815633972
%C A296834 .55..793.11475.192730..3017667..48122349..768117235..12228697715..194991656916
%C A296834 .89.1782.35054.826498.17931240.397252886.8815633972.194991656916.4321362259224
%H A296834 R. H. Hardin, <a href="/A296834/b296834.txt">Table of n, a(n) for n = 1..199</a>
%F A296834 Empirical for column k:
%F A296834 k=1: a(n) = a(n-1) +a(n-2)
%F A296834 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3)
%F A296834 k=3: [order 15]
%F A296834 k=4: [order 50]
%e A296834 Some solutions for n=5 k=4
%e A296834 ..0..0..1..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1
%e A296834 ..1..0..1..1. .1..1..1..1. .0..0..1..0. .0..0..0..0. .0..1..0..0
%e A296834 ..0..0..0..0. .1..1..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0
%e A296834 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..1. .0..1..0..0
%e A296834 ..0..0..1..0. .0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..1
%Y A296834 Column 1 is A000045(n+2).
%Y A296834 Column 2 is A006356.
%K A296834 nonn,tabl
%O A296834 1,1
%A A296834 _R. H. Hardin_, Dec 21 2017