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Number of non-collinear triples in a 5 X n rectangular grid.
2

%I #19 Jun 20 2020 14:14:41

%S 0,100,412,1056,2148,3820,6176,9352,13456,18612,24940,32568,41596,

%T 52164,64384,78376,94256,112156,132180,154464,179116,206260,236016,

%U 268512,303848,342164,383572,428192,476140,527548,582520,641192,703672,770084,840548,915192,994116

%N Number of non-collinear triples in a 5 X n rectangular grid.

%H Giovanni Resta, <a href="/A334707/b334707.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,-1,1,-1,2,-1).

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

%F G.f.: 4*x*(25 + 53*x + 83*x^2 + 87*x^3 + 67*x^4 + 35*x^5 + 10*x^6)/((1 - x)^4*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-5) + a(n-6) - a(n-7) + 2*a(n-8) - a(n-9) for n > 9. (End)

%Y A row of A334705.

%K nonn

%O 1,2

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

%E Terms a(6) and beyond from _Giovanni Resta_, Jun 20 2020