A295120 - OEIS

%I #4 Nov 15 2017 06:21:58

%S 1,2,2,3,5,3,4,9,9,4,6,20,26,20,6,9,41,77,77,41,9,13,85,226,326,226,

%T 85,13,19,178,665,1373,1373,665,178,19,28,369,1960,5793,8257,5793,

%U 1960,369,28,41,769,5769,24347,49302,49302,24347,5769,769,41,60,1600,16983,102398

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

%C Table starts

%C ..1...2.....3......4........6.........9.........13...........19............28

%C ..2...5.....9.....20.......41........85........178..........369...........769

%C ..3...9....26.....77......226.......665.......1960.........5769.........16983

%C ..4..20....77....326.....1373......5793......24347.......102398........431050

%C ..6..41...226...1373.....8257.....49302.....295083......1768323......10586331

%C ..9..85...665...5793....49302....420519....3590821.....30650456.....261518933

%C .13.178..1960..24347...295083...3590821...43655680....530696748....6452840307

%C .19.369..5769.102398..1768323..30650456..530696748...9196006628..159316011413

%C .28.769.16983.431050.10586331.261518933.6452840307.159316011413.3931962260999

%H R. H. Hardin, <a href="/A295120/b295120.txt">Table of n, a(n) for n = 1..391</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)

%F k=3: [order 10]

%F k=4: [order 14]

%F k=5: [order 40]

%F k=6: [order 78]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000930(n+1).

%Y Column 2 is A105309(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 15 2017