A269075 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.
2, 4, 4, 7, 11, 8, 13, 27, 32, 16, 23, 76, 123, 89, 32, 41, 185, 521, 537, 244, 64, 72, 489, 1887, 3288, 2343, 659, 128, 126, 1204, 7477, 17713, 20400, 10167, 1760, 256, 219, 3059, 27042, 102545, 165607, 123976, 43959, 4657, 512, 379, 7539, 102070, 542112
Offset: 1
Examples
Some solutions for n=4 k=4 ..1..0..0..0. .0..1..1..0. .1..0..0..1. .0..0..0..1. .0..1..0..1 ..0..0..0..0. .0..0..0..0. .1..0..1..0. .0..0..0..1. .0..1..0..1 ..1..0..0..0. .1..0..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..0 ..0..0..0..1. .1..0..0..1. .0..0..0..0. .1..0..1..0. .0..0..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..721
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)
k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7
k=5: [order 12]
k=6: [order 14]
k=7: [order 24] for n>25
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
n=2: a(n) = 2*a(n-1) +5*a(n-2) -6*a(n-3) -9*a(n-4)
n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)
n=4: [order 8]
n=5: [order 14]
Comments