A205066 - OEIS

A205066

Number of (n+1) X 3 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors.

%I #10 Jun 10 2018 17:33:03

%S 40,64,90,146,244,386,638,1018,1666,2676,4360,7024,11418,18420,29882,

%T 48272,78228,126456,204798,331194,536146,867282,1403624,2270906,

%U 3674698,5945848,9620410,15567302,25186452,40757134,65938814,106705842,172629762

%N Number of (n+1) X 3 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors.

%C Column 2 of A205072.

%H R. H. Hardin, <a href="/A205066/b205066.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-2) - a(n-6) - 4*a(n-8) - a(n-10) + a(n-12) for n > 14.

%F Empirical g.f.: 2*x*(20 + 32*x - 15*x^2 - 23*x^3 - 13*x^4 - 26*x^5 - 27*x^6 - 38*x^7 + x^8 + 12*x^9 + 3*x^10 + 15*x^11 + x^12 - 4*x^13) / ((1 + x - x^2)*(1 - x + x^2)*(1 - x - x^2)*(1 + x + x^2)*(1 - x^2 - x^4)). - _Colin Barker_, Jun 10 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A205072.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 21 2012