A211912 - OEIS

%I #7 Jul 20 2018 09:36:51

%S 0,1,10,214,1946,10431,40561,127275,342434,820396,1794811,3649471,

%T 6986365,12714404,22162596,37221766,60519231,95631155,147337624,

%U 221925796,327546796,474632341,676377395

%N 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 Column 2 of A211916.

%F 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 Conjectures from _Colin Barker_, Jul 20 2018: (Start)

%F 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 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 (End)

%e Some solutions for n=4:

%e ..0........0........0........0........0........0........0........0

%e ..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2

%e ..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 ..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 Cf. A211916.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 25 2012