A231645 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.
3, 35, 104, 341, 1189, 4040, 13560, 45803, 155131, 524683, 1773770, 5998876, 20290918, 68629108, 232120783, 785115525, 2655576210, 8982247095, 30381769982, 102764504913, 347595681724, 1175726561166, 3976846922803, 13451535863780
Offset: 1
Keywords
Examples
Some solutions for n=3: ..1..1....2..2....0..0....1..1....1..2....0..0....0..0....0..0....2..0....0..1 ..2..1....1..1....0..2....2..2....0..0....2..1....0..0....0..0....2..0....0..0 ..1..1....1..1....0..0....1..1....0..0....0..0....2..1....1..2....0..0....1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A231651.
Formula
Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 19*a(n-3) - 32*a(n-4) + 15*a(n-5) - 13*a(n-6) + 13*a(n-7) + 10*a(n-8) + 7*a(n-9) + 5*a(n-10) + a(n-11) for n>12.
Empirical g.f.: x*(3 + 17*x - 70*x^2 + 80*x^3 - 178*x^4 + 97*x^5 - 49*x^6 + 100*x^7 + 73*x^8 + 48*x^9 + 31*x^10 + 6*x^11) / (1 - 6*x + 12*x^2 - 19*x^3 + 32*x^4 - 15*x^5 + 13*x^6 - 13*x^7 - 10*x^8 - 7*x^9- 5*x^10 - x^11). - Colin Barker, Mar 18 2018
Comments