A280550 - OEIS

%I #7 Feb 13 2019 11:33:49

%S 1,34,144,382,832,1666,3182,5886,10680,19122,33920,59754,104690,

%T 182598,317264,549398,948528,1633186,2805094,4807006,8220440,14030634,

%U 23904656,40659818,69051850,117099910,198312144,335420782,566645728,956190466

%N Number of n X 4 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A280550/b280550.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>11.

%F Empirical g.f.: x*(1 + 28*x - 48*x^2 - 79*x^3 + 86*x^4 + 142*x^5 - 57*x^6 - 134*x^7 + 46*x^8 + 39*x^9 - 36*x^10) / ((1 - x)^3*(1 - x - x^2)^3). - _Colin Barker_, Feb 13 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A280554.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 05 2017