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%I #23 Nov 29 2016 07:07:08
%S 0,1,126,1820,12650,58905,211876,635376,1663740,3921225,8495410,
%T 17178876,32795126,59626385,103962600,174792640,284660376,450710001,
%U 695946630,1050739900,1554599970,2258257001,3226076876,4538847600,6296972500,8624108025,11671285626
%N Number of ways to choose four points in an n X n grid (or geoplane).
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1)
%F a(n) = binomial(n^2,4) = (1/24)*n^2*(n^2-1)*(n^2-2)*(n^2-3).
%F G.f.: x^2*(1+x)*(1+116*x+606*x^2+116*x^3+x^4)/(1-x)^9. - _Colin Barker_, Jan 19 2012
%p a:= proc(n) binomial(n^2, 4) end: seq(a(n), n=1..35);
%o (Maxima)
%o makelist(binomial(n^2, 4), n, 1, 56); /* _Martin Ettl_, Oct 15 2012 */
%Y Cf. A175383, A189346.
%K nonn,easy
%O 1,3
%A _Martin Renner_, Apr 20 2011
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