A302309 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 13, 10, 16, 13, 31, 26, 33, 21, 32, 21, 113, 48, 66, 58, 42, 64, 34, 363, 121, 194, 153, 153, 86, 128, 55, 813, 275, 663, 445, 380, 336, 179, 256, 89, 1751, 600, 2048, 1595, 1271, 1090, 937, 370, 512, 144, 5001, 1296, 5790, 4772, 5715
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1 ..0..1..0..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1 ..0..1..0..1. .0..1..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0 ..0..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1 ..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..220
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 60] for n>61
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 15] for n>16
n=4: [order 61] for n>64
Comments