cp's OEIS Frontend

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.

%I A211912 #7 Jul 20 2018 09:36:51
%S A211912 0,1,10,214,1946,10431,40561,127275,342434,820396,1794811,3649471,
%T A211912 6986365,12714404,22162596,37221766,60519231,95631155,147337624,
%U A211912 221925796,327546796,474632341,676377395
%N 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.
%C A211912 Column 2 of A211916.
%F A211912 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.
%F A211912 Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F A211912 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.
%F A211912 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.
%F A211912 (End)
%e A211912 Some solutions for n=4:
%e A211912 ..0........0........0........0........0........0........0........0
%e A211912 ..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
%e A211912 ..3.4.1....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5....3.4.5....3.4.5
%e A211912 ..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
%Y A211912 Cf. A211916.
%K A211912 nonn
%O A211912 1,3
%A A211912 _R. H. Hardin_, Apr 25 2012