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Number of collinear triples in a 4 X n rectangular grid.
2

%I #16 Jun 20 2020 14:14:30

%S 4,8,20,44,84,140,224,332,472,648,864,1120,1428,1784,2196,2668,3204,

%T 3804,4480,5228,6056,6968,7968,9056,10244,11528,12916,14412,16020,

%U 17740,19584,21548,23640,25864,28224,30720,33364,36152,39092,42188,45444,48860,52448,56204

%N Number of collinear triples in a 4 X n rectangular grid.

%H Giovanni Resta, <a href="/A334706/b334706.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,-1,0,2,-1).

%F From _Stefano Spezia_, Jun 20 2020: (Start)

%F G.f.: 4*x*(1 + x^2 + 2*x^3 + 2*x^4)/((1 - x)^4*(1 + 2*x + 2*x^2 + x^3)).

%F a(n) = 2*a(n-1) - a(n-3) - a(n-4) + 2*a(n-6) - a(n-7) for n > 7. (End)

%Y A column of A334704.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 13 2020

%E Terms a(8) and beyond from _Giovanni Resta_, Jun 20 2020