A211912 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-3.
0, 1, 10, 214, 1946, 10431, 40561, 127275, 342434, 820396, 1794811, 3649471, 6986365, 12714404, 22162596, 37221766, 60519231, 95631155, 147337624, 221925796, 327546796, 474632341, 676377395
Offset: 1
Keywords
Examples
Some solutions for n=4: ..0........0........0........0........0........0........0........0 ..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2 ..3.4.1....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5....3.4.5....3.4.5 ..2.5.6.7..6.0.1.7..6.1.7.2..6.2.7.3..5.6.7.2..6.7.0.8..5.6.3.7..0.1.6.7
Crossrefs
Cf. A211916.
Formula
Empirical: a(n) = (1/128)*n^8 + (1/32)*n^7 - (53/192)*n^6 - (5/16)*n^5 + (513/128)*n^4 - (577/96)*n^3 - (215/96)*n^2 + (235/24)*n - 4 for n>1.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x^2*(1 + x + 160*x^2 + 296*x^3 - 93*x^4 - 104*x^5 + 66*x^6 - 13*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.
(End)
Comments