A303040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 14, 10, 16, 13, 31, 28, 35, 21, 32, 21, 113, 56, 74, 71, 42, 64, 34, 363, 150, 234, 197, 186, 86, 128, 55, 813, 360, 869, 703, 544, 459, 179, 256, 89, 1751, 828, 2926, 3069, 2494, 1686, 1287, 370, 512, 144, 5001, 1906, 8500, 11079
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1 ..0..0..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0 ..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .1..1..0..1 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1 ..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..0..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..219
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 70]
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 11] for n>12
n=4: [order 61] for n>62
Comments