A297720 - OEIS

%I #4 Jan 04 2018 21:59:14

%S 1,2,1,4,10,1,7,34,29,1,12,83,145,87,1,21,258,523,747,280,1,37,865,

%T 2717,4212,4090,876,1,65,2651,14462,36981,34319,21116,2735,1,114,8041,

%U 68919,336653,512354,268630,110551,8583,1,200,25114,332306,2699832,8103241

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

%C Table starts

%C .1.....2.......4.........7..........12............21..............37

%C .1....10......34........83.........258...........865............2651

%C .1....29.....145.......523........2717.........14462...........68919

%C .1....87.....747......4212.......36981........336653.........2699832

%C .1...280....4090.....34319......512354.......8103241.......107787351

%C .1...876...21116....268630.....6812856.....183324631......4021047904

%C .1..2735..110551...2139403....91994155....4238895126....154327332017

%C .1..8583..582755..17031173..1242370107...98184350818...5920531350715

%C .1.26900.3055652.135252357.16741579726.2265008802005.226188909640209

%H R. H. Hardin, <a href="/A297720/b297720.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) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)

%F k=3: [order 13]

%F k=4: [order 42]

%F k=5: [order 87]

%F Empirical for row n:

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

%F n=2: a(n) = 4*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4) -24*a(n-5) +24*a(n-6)

%F n=3: [order 18]

%F n=4: [order 51]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 2 is A295525.

%Y Row 1 is A005251(n+2).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 04 2018