A281475 - OEIS

A281475

Number of 7 X n 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I #8 Feb 20 2019 05:30:15

%S 64,2785,634,897,1106,1422,1887,2429,3093,4063,5629,8037,11711,17407,

%T 26039,38977,58581,88383,133531,201957,305881,463585,702653,1065249,

%U 1615351,2449669,3715009,5634375,8545763,12961559,19659317,29818565

%N Number of 7 X n 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281475/b281475.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-7) - a(n-8) for n>16.

%F Empirical g.f.: x*(64 + 2657*x - 4872*x^2 + 2350*x^3 - 2775*x^4 + 2258*x^5 - 114*x^6 - 196*x^7 - 2915*x^8 + 1992*x^9 - 209*x^10 - 31*x^11 - 20*x^12 - 9*x^13 - 14*x^14 - 32*x^15) / ((1 - x)*(1 - x - x^3 - x^7)). - _Colin Barker_, Feb 20 2019

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Row 7 of A281469.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2017