A202974 Number of n X 3 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.
1, 4, 17, 58, 215, 866, 3507, 14120, 56921, 229860, 928443, 3749720, 15144167, 61165438, 247041429, 997775144, 4029911351, 16276407572, 65738788527, 265512410122, 1072378133103, 4331228325504, 17493399301365, 70654095337584
Offset: 1
Keywords
Examples
Some solutions for n=5: 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A202979.
Formula
Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 16*a(n-3) - 14*a(n-4) - 3*a(n-5) + 8*a(n-6) - 9*a(n-7) - 2*a(n-8) + 6*a(n-9) + 2*a(n-10).
Empirical g.f.: x*(1 - 2*x + 4*x^2 - 16*x^3 + 4*x^4 + x^5 - 10*x^6 + 4*x^7 + 8*x^8 + 2*x^9) / (1 - 6*x + 11*x^2 - 16*x^3 + 14*x^4 + 3*x^5 - 8*x^6 + 9*x^7 + 2*x^8 - 6*x^9 - 2*x^10). - Colin Barker, Jun 03 2018
Comments