cp's OEIS Frontend

A183337 Number of n X 5 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

%I A183337 #12 Mar 28 2018 08:13:50
%S A183337 1,6,13,26,72,175,407,1005,2450,5893,14318,34780,84221,204245,495483,
%T A183337 1201256,2912843,7064014,17129250,41536473,100724269,244248135,
%U A183337 592280544,1436238121,3482767494,8445435610,20479537209,49661306333,120424822297
%N A183337 Number of n X 5 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.
%C A183337 Equivalent to all 1s connected only in 2 X 2 blocks.
%C A183337 Column 5 of A183342.
%H A183337 R. H. Hardin, <a href="/A183337/b183337.txt">Table of n, a(n) for n = 1..200</a>
%F A183337 Empirical: a(n) = a(n-1) + a(n-2) + 5*a(n-3) + 2*a(n-4) + a(n-5) - a(n-7) - a(n-8).
%F A183337 Empirical g.f.: x*(1 + 5*x + 6*x^2 + 2*x^3 + x^4 - x^5 - 2*x^6 - x^7) / (1 - x - x^2 - 5*x^3 - 2*x^4 - x^5 + x^7 + x^8). - _Colin Barker_, Mar 27 2018
%e A183337 Some solutions for 7 X 5:
%e A183337   1 1 0 0 0    0 0 0 1 1    0 0 1 1 0    0 0 1 1 0
%e A183337   1 1 0 0 0    0 0 0 1 1    0 0 1 1 0    0 0 1 1 0
%e A183337   0 0 1 1 0    0 0 0 0 0    1 1 0 0 0    0 0 0 0 0
%e A183337   0 0 1 1 0    0 0 0 0 0    1 1 0 0 0    1 1 0 1 1
%e A183337   0 0 0 0 0    0 0 1 1 0    0 0 0 0 0    1 1 0 1 1
%e A183337   1 1 0 0 0    0 0 1 1 0    0 0 0 1 1    0 0 0 0 0
%e A183337   1 1 0 0 0    0 0 0 0 0    0 0 0 1 1    0 0 0 0 0
%Y A183337 Cf. A183342.
%K A183337 nonn
%O A183337 1,2
%A A183337 _R. H. Hardin_, Jan 04 2011