%I #23 Sep 08 2022 08:45:05
%S 12,110,926,7556,60920,488860,3915640,31340216,250769592,2006308480,
%T 16050948896,128409116176,1027277763840,8218237436320,65745948074080,
%U 525967738606656,4207742397091072,33661940724484800,269295530702399616
%N Number of n X 3 binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.
%H G. C. Greubel, <a href="/A069294/b069294.txt">Table of n, a(n) for n = 2..1001</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-34,14,16).
%F G.f.: 2*x^2*(6-17*x+7*x^2+8*x^3)/(1-8*x)/(2*x^3+2*x^2-4*x+1). - _Vladeta Jovovic_, Jul 02 2003
%t LinearRecurrence[{12, -34, 14, 16}, {12, 110, 926, 7556}, 50] (* _G. C. Greubel_, Apr 22 2018 *)
%o (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 16,14,-34,12]^(n-2)*[12;110;926;7556])[1,1] \\ _Charles R Greathouse IV_, May 10 2016
%o (PARI) x='x+O('x^30); Vec(2*x^2*(6-17*x+7*x^2+8*x^3)/((1-8*x)*(2*x^3 +2*x^2-4*x+1))) \\ _G. C. Greubel_, Apr 22 2018
%o (Magma) I:=[12, 110, 926, 7556]; [n le 4 select I[n] else 12*Self(n-1) - 34*Self(n-2) +14*Self(n-3) + 16*Self(n-4): n in [1..30]]; // _G. C. Greubel_, Apr 22 2018
%Y Cf. n X 2 A002450, n X 4 A069295, n X 5 A069296, n X 6 A069297, n X 7 A069298, n X 8 A069299, n X 9 A069300, n X 10 A069301, n X 11 A069302, n X 12 A069303, n X 13 A069304, n X 14 A069305, read by rows A069306-A069320.
%K nonn,easy
%O 2,1
%A _R. H. Hardin_, Mar 14 2002