|
%I #4 Apr 09 2018 09:24:48
%S 0,1,0,1,3,0,2,7,10,0,3,10,28,23,0,5,27,42,115,61,0,8,45,100,168,497,
%T 162,0,13,98,290,539,902,2086,421,0,21,193,730,1977,3683,3256,9091,
%U 1103,0,34,379,1700,5942,23909,17546,15852,40575,2890,0,55,778,4246,16733,128242
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0....1......1......2.......3.........5..........8..........13...........21
%C .0....3......7.....10......27........45.........98.........193..........379
%C .0...10.....28.....42.....100.......290........730........1700.........4246
%C .0...23....115....168.....539......1977.......5942.......16733........49219
%C .0...61....497....902....3683.....23909.....128242......465323......1918153
%C .0..162...2086...3256...17546....182773....1275348.....5557469.....29725028
%C .0..421...9091..15852...92603...1551340...16130212....82774516....506265517
%C .0.1103..40575..77904..615351..18089458..303355178..1916999716..16636194027
%C .0.2890.172996.314276.3268978.155010391.3654880956.27228654766.305442540368
%H R. H. Hardin, <a href="/A302528/b302528.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
%F k=3: [order 18]
%F k=4: [order 72]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F n=3: [order 15] for n>17
%F n=4: [order 68] for n>69
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..1. .0..0..1..1
%e ..1..1..0..0. .1..0..1..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
%e ..1..0..1..0. .0..1..0..1. .1..0..1..0. .1..1..1..1. .1..1..1..1
%e ..0..0..1..1. .1..1..1..0. .1..0..0..1. .1..1..1..1. .0..0..1..1
%e ..1..1..0..0. .0..0..0..1. .0..1..1..0. .1..0..0..1. .1..1..0..0
%Y Column 2 is A185828.
%Y Row 1 is A000045(n-1).
%Y Row 2 is A302279.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Apr 09 2018
| 