A207452 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
42, 1764, 10710, 36456, 92610, 196812, 370734, 640080, 1034586, 1588020, 2338182, 3326904, 4600050, 6207516, 8203230, 10645152, 13595274, 17119620, 21288246, 26175240, 31858722, 38420844, 45947790, 54529776, 64261050, 75239892, 87568614
Offset: 1
Keywords
Examples
Some solutions for n=5: 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A207453.
Formula
Empirical: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n.
Conjectures from Colin Barker, Jun 23 2018: (Start)
G.f.: 42*x*(1 + 37*x + 55*x^2 + 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
Comments