A302877 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 17, 10, 16, 13, 31, 35, 37, 21, 32, 21, 113, 72, 95, 82, 42, 64, 34, 363, 241, 306, 285, 209, 86, 128, 55, 813, 722, 1442, 1197, 858, 536, 179, 256, 89, 1751, 1821, 5871, 7580, 4849, 2938, 1549, 370, 512, 144, 5001, 4863, 21832, 41498
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1 ..1..0..1..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..1..0..1 ..1..0..1..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..1..0..1 ..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..1 ..1..1..0..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .1..1..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..180
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 56] for n>59
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 60] for n>64
Comments