A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 148, 128, 16, 32, 263, 748, 884, 512, 32, 64, 855, 3657, 7070, 5296, 2048, 64, 128, 2778, 18108, 54177, 67070, 31760, 8192, 128, 256, 9027, 89658, 420121, 807601, 636852, 190528, 32768, 256, 512, 29333, 444359
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0 ..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..0..1..0. .0..1..1..1 ..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0 ..1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0. .0..0..1..0 ..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..0..0..1. .0..0..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..311
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3
k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6
k=5: [order 11] for n>13
k=6: [order 25] for n>27
k=7: [order 53] for n>56
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 15] for n>18
n=4: [order 53] for n>58
Comments