A301951 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
0, 1, 0, 1, 2, 0, 2, 5, 5, 0, 3, 16, 20, 13, 0, 5, 52, 123, 83, 34, 0, 8, 169, 680, 947, 342, 89, 0, 13, 549, 4070, 9084, 7326, 1411, 233, 0, 21, 1784, 23565, 98839, 120815, 56710, 5820, 610, 0, 34, 5797, 138014, 1029960, 2406169, 1608681, 439078, 24007, 1597, 0
Offset: 1
Examples
Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1 ..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..1..0..1 ..0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..1..0. .0..0..1..0 ..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0 ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..364
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 4*a(n-1) +a(n-2) -2*a(n-3)
k=4: a(n) = 9*a(n-1) -8*a(n-2) -14*a(n-3) +4*a(n-4) +4*a(n-5) -a(n-6)
k=5: [order 13] for n>15
k=6: [order 26] for n>28
k=7: [order 43] for n>47
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 10] for n>12
n=4: [order 36] for n>40
Comments