A218659 Hilltop maps: number of n X 4 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..1 n X 4 array.
9, 225, 3249, 50625, 793881, 12383361, 193349025, 3018953025, 47135449449, 735942652641, 11490533873361, 179405691966081, 2801123686963449, 43734921492423681, 682848585990347841, 10661553197658712449
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..1..0..1....1..0..1..0....0..0..0..0....1..0..0..0....1..1..1..1 ..0..1..0..1....1..1..0..0....0..1..0..1....1..0..1..0....1..0..0..1 ..0..0..0..1....0..0..0..1....0..1..1..1....0..1..1..1....0..1..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A218663.
Formula
Empirical: a(n) = 12*a(n-1) +45*a(n-2) +180*a(n-3) -27*a(n-4) -81*a(n-6).
Empirical g.f.: 9*x*(1 - x)*(1 + 14*x + 30*x^2 + 18*x^3 + 9*x^4) / ((1 + 3*x + 9*x^2 - 9*x^3)*(1 - 15*x - 9*x^2 - 9*x^3)). - Colin Barker, Mar 10 2018
Comments