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A209646 Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A209646 #18 Oct 19 2022 08:06:49
%S A209646 9,81,270,630,1215,2079,3276,4860,6885,9405,12474,16146,20475,25515,
%T A209646 31320,37944,45441,53865,63270,73710,85239,97911,111780,126900,143325,
%U A209646 161109,180306,200970,223155,246915,272304,299376,328185,358785,391230
%N A209646 Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A209646 Column 4 of A209650.
%H A209646 R. H. Hardin, <a href="/A209646/b209646.txt">Table of n, a(n) for n = 1..210</a>
%H A209646 Robert Israel, <a href="/A209646/a209646.pdf">Maple-assisted proof of formula</a>
%H A209646 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A209646 Empirical: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n.
%F A209646 Formula confirmed by _Robert Israel_, Mar 07 2018: see link.
%F A209646 From _Colin Barker_, Jul 12 2018: (Start)
%F A209646 G.f.: 9*x*(1 + 5*x) / (1 - x)^4.
%F A209646 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A209646 (End)
%e A209646 Some solutions for n=4:
%e A209646   0 1 0 1    0 1 1 0    0 0 0 0    1 0 1 0    1 0 1 1
%e A209646   0 0 0 0    1 1 0 1    0 0 0 0    0 1 1 0    0 1 1 0
%e A209646   0 0 0 0    0 1 0 1    0 0 0 0    0 0 0 0    0 1 1 0
%e A209646   0 0 0 0    0 1 0 1    0 0 0 0    0 0 0 0    0 1 1 0
%p A209646 seq(9*n^3 + (9/2)*n^2 - (9/2)*n, n=1..100); # _Robert Israel_, Mar 07 2018
%o A209646 (PARI) Vec(9*x*(1 + 5*x) / (1 - x)^4 + O(x^40)) \\ _Colin Barker_, Jul 12 2018
%o A209646 (PARI) a(n) = 9*n^3+(9/2)*n^2-(9/2)*n; \\ _Altug Alkan_, Jul 12 2018
%Y A209646 Cf. A209650.
%K A209646 nonn,easy
%O A209646 1,1
%A A209646 _R. H. Hardin_, Mar 11 2012