A198655 Number of n X 1 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.
0, 1, 1, 2, 3, 6, 11, 23, 47, 103, 226, 518, 1200, 2867, 6946, 17234, 43393, 111418, 290233, 768819, 2064637, 5626757, 15531220, 43432402, 122878654, 351665399, 1016952840, 2970387672, 8755225931, 26027153206, 77972236615, 235260594303
Offset: 1
Keywords
Examples
All solutions for n=5: ..0....0....0 ..0....0....0 ..0....1....0 ..0....1....1 ..0....1....1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A198661.
Formula
Empirical: a(n) = 7*a(n-1) + a(n-2) - 97*a(n-3) + 105*a(n-4) + 531*a(n-5) - 757*a(n-6) - 1511*a(n-7) + 2143*a(n-8) + 2457*a(n-9) - 2689*a(n-10) - 2227*a(n-11) + 1198*a(n-12) + 840*a(n-13) for n>14.
Empirical g.f.: x^2*(1 - 6*x - 6*x^2 + 85*x^3 - 25*x^4 - 476*x^5 + 247*x^6 + 1348*x^7 - 523*x^8 - 1959*x^9 + 157*x^10 + 1157*x^11 + 309*x^12) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)*(1 - x - 5*x^2)*(1 - x - 7*x^2)). - Colin Barker, Mar 02 2018
Comments