Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Feb 17 2018 10:26:02
%S 1,18,129,899,6205,43066,298361,2068149,14334327,99354814,688646455,
%T 4773147461,33083623049,229309139316,1589386941041,11016355018433,
%U 76356533603993,529242224053012,3668282443014641,25425590535640541
%N Number of n X 3 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Column 3 of A299142.
%H R. H. Hardin, <a href="/A299137/b299137.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +8*a(n-2) -12*a(n-3) +8*a(n-4) +7*a(n-5) -4*a(n-6) -2*a(n-7) -7*a(n-8) -5*a(n-9) +2*a(n-10) for n>11.
%F Empirical g.f.: x*(1 + 12*x + 13*x^2 - 7*x^3 - 13*x^4 + 41*x^5 - 41*x^6 - 106*x^7 - 37*x^8 + 14*x^9 + 2*x^10) / ((1 - x)*(1 - 5*x - 13*x^2 - x^3 - 9*x^4 - 16*x^5 - 12*x^6 - 10*x^7 - 3*x^8 + 2*x^9)). - _Colin Barker_, Feb 17 2018
%e Some solutions for n=5:
%e ..0..0..1. .0..0..0. .0..1..1. .0..1..1. .0..0..1. .0..1..1. .0..0..1
%e ..1..0..1. .0..1..0. .0..1..0. .0..0..1. .1..1..0. .1..0..0. .0..0..1
%e ..1..1..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1. .0..1..1. .1..0..1
%e ..1..0..0. .1..1..0. .0..0..0. .1..0..1. .0..1..0. .0..0..1. .0..1..0
%e ..0..1..1. .1..0..1. .0..0..0. .1..1..0. .1..0..1. .1..1..1. .1..0..0
%Y Cf. A299142.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 03 2018