login

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”).

Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
1

%I #11 Feb 15 2018 12:17:15

%S 8,8,19,53,113,256,541,1148,2488,5349,11453,24617,52916,113605,243988,

%T 524156,1125805,2417997,5193737,11155712,23961101,51466060,110544232,

%U 237437573,509991637,1095411153,2352832580,5053645925,10854721796

%N Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 5 of A299595.

%H R. H. Hardin, <a href="/A299592/b299592.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(8 + 3*x^2 + 2*x^3 + 9*x^4 + 33*x^5 + 10*x^6 - 14*x^7 - 10*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Feb 15 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A299595.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2018