A202195 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.
108, 240, 450, 756, 1176, 1728, 2430, 3300, 4356, 5616, 7098, 8820, 10800, 13056, 15606, 18468, 21660, 25200, 29106, 33396, 38088, 43200, 48750, 54756, 61236, 68208, 75690, 83700, 92256, 101376, 111078, 121380, 132300, 143856, 156066, 168948
Offset: 1
Keywords
Examples
Some solutions for n=10: 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A202202.
Formula
Empirical: a(n) = 3*(n+3)*(n+2)^2 = 3*A011379(n+2).
Conjectures from Colin Barker, Mar 03 2018: (Start)
G.f.: 6*x*(18 - 32*x + 23*x^2 - 6*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
Comments