A297733 - OEIS

%I #4 Jan 04 2018 22:18:00

%S 1,1,1,1,2,1,1,8,3,1,1,15,17,4,1,1,32,34,39,6,1,1,61,92,93,151,9,1,1,

%T 145,223,362,502,385,13,1,1,297,700,1103,2719,1443,1026,19,1,1,658,

%U 1747,4795,11341,11171,4676,3272,28,1,1,1352,4931,15646,82549,65215,53173,19601

%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 4 neighboring 1s.

%C Table starts

%C .1..1....1.....1.......1........1.........1...........1............1

%C .1..2....8....15......32.......61.......145.........297..........658

%C .1..3...17....34......92......223.......700........1747.........4931

%C .1..4...39....93.....362.....1103......4795.......15646........61063

%C .1..6..151...502....2719....11341.....82549......396787......2346541

%C .1..9..385..1443...11171....65215....673171.....4414693.....36515720

%C .1.13.1026..4676...53173...414651...6241242....56834907....675663465

%C .1.19.3272.19601..304157..3199929..74469526...959915987..16537401517

%C .1.28.8945.62749.1417699.21221319.718454750.13045679082.322119198752

%H R. H. Hardin, <a href="/A297733/b297733.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +a(n-2) +13*a(n-3) -2*a(n-4) +4*a(n-5) -11*a(n-6) -3*a(n-7) -a(n-8)

%F k=4: [order 19]

%F k=5: [order 35]

%F Empirical for row n:

%F n=1: a(n) = a(n-1)

%F n=2: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) +6*a(n-4) -6*a(n-5)

%F n=3: [order 9]

%F n=4: [order 27]

%F n=5: [order 80]

%e Some solutions for n=6 k=4

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

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

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

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

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

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

%Y Column 2 is A000930(n+1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 04 2018