A281402 - OEIS

%I #7 Feb 19 2019 09:20:34

%S 0,6,131,314,689,1294,2364,4338,7850,14150,25510,45790,81958,146454,

%T 261006,464062,823590,1458790,2579102,4552526,8023638,14120758,

%U 24818318,43566366,76387782,133790726,234092798,409199086,714645558,1247036630

%N Number of 3 X n 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281402/b281402.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 8*a(n-3) - 13*a(n-4) + 12*a(n-5) -8*a(n-6) +8*a(n-7) -4*a(n-8) for n>13.

%F Empirical g.f.: x^2*(6 + 107*x - 174*x^2 + 171*x^3 - 548*x^4 + 441*x^5 - 308*x^6 + 519*x^7 - 92*x^8 + 34*x^9 - 28*x^10 - 32*x^11) / ((1 - x)^2*(1 - x - 2*x^3)^2). - _Colin Barker_, Feb 19 2019

%e Some solutions for n=4:

%e ..0..0..1..0. .0..0..1..0. .0..0..0..1. .0..1..1..0. .0..0..1..0

%e ..1..0..1..0. .0..1..1..0. .1..1..0..1. .1..0..0..0. .1..0..1..1

%e ..0..1..1..0. .1..0..0..1. .1..1..0..0. .1..0..1..0. .0..0..1..0

%Y Row 3 of A281400.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 21 2017