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%I #12 Dec 07 2020 16:42:06
%S 8,192,3344,52800,806168,12166272,182871584,2744987520,41184460328,
%T 617815378752,9267473759024,139013323899840,2085205952447288,
%U 31278119775589632,469171949135641664,7037579999715797760,105563703809659391048,1583455576216052670912,23751833738601248135504,356277506555834959529280
%N a(n) is the area of the n-gon with vertices (3^i, 5^i) for 0 <= i <= n-1.
%H Robert Israel, <a href="/A339487/b339487.txt">Table of n, a(n) for n = 3..851</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24, -158, 360, -225).
%F a(n) = -1/14 - 5^n/10 + 3^n/6 + 15^n/210.
%F G.f.: 8*x^3/(225*x^4-360*x^3+158*x^2-24*x+1).
%e a(3) is the area of the triangle with vertices (1,1), (3,5) and (9,25), which is 8.
%p f:= n -> -1/14 - 5^n/10 + 3^n/6 + 15^n/210:
%p map(f, [$3..30]);
%t Drop[CoefficientList[Series[8 x^3/(225 x^4 - 360 x^3 + 158 x^2 - 24 x + 1), {x, 0, 22}], x], 3] (* _Michael De Vlieger_, Dec 07 2020 *)
%K nonn
%O 3,1
%A _J. M. Bergot_ and _Robert Israel_, Dec 07 2020