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A188707 Number of 3 X n binary arrays without the pattern 0 0 diagonally or vertically.

%I A188707 #39 Mar 21 2021 05:32:49
%S A188707 5,21,90,387,1665,7164,30825,132633,570690,2455551,10565685,45461772,
%T A188707 195611805,841673709,3621533130,15582644523,67048623225,288495182556,
%U A188707 1241330043105,5341164667857,22981833209970,98885672046279
%N A188707 Number of 3 X n binary arrays without the pattern 0 0 diagonally or vertically.
%C A188707 Row 3 of A188706.
%H A188707 R. H. Hardin, <a href="/A188707/b188707.txt">Table of n, a(n) for n = 1..200</a>
%H A188707 C. Bautista-Ramos and C. Guillen-Galvan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Bautista/bautista4.html">Fibonacci numbers of generalized Zykov sums</a>, J. Integer Seq., 15 (2012), #12.7.8.
%H A188707 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3).
%F A188707 a(n) = 5*a(n-1) - 3*a(n-2).
%F A188707 a(n) = [1,1;1,4]^(n-1).{1,2}.{1,2}. - _John M. Campbell_, Jul 09 2011
%F A188707 G.f.: x*(5 - 4*x)/(1 - 5*x + 3*x^2). - _Colin Barker_, Mar 11 2012
%e A188707 Some solutions for 3 X 3:
%e A188707   1 1 0    1 0 0    1 1 0    1 0 0    0 0 0    1 0 0    0 0 1
%e A188707   1 1 1    1 1 1    1 0 1    1 1 1    1 1 1    1 1 1    1 1 1
%e A188707   1 0 1    1 1 0    0 1 1    0 0 1    0 0 1    1 1 1    0 1 1
%t A188707 LinearRecurrence[{5, -3}, {5, 21}, 22] (* _Robert G. Wilson v_, Jul 13 2011 *)
%o A188707 (PARI)  \\ using formula by _John M. Campbell_
%o A188707 a(n)=my(v=[1,1;1,4]^(n-1)*[1,2]~); v[1]*1+v[2]*2; \\ _Joerg Arndt_, Mar 19 2021
%K A188707 nonn,easy
%O A188707 1,1
%A A188707 _R. H. Hardin_, Apr 08 2011