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%I #17 Dec 26 2021 20:47:07
%S 0,100,300,600,1000,1500,2100,2800,3600,4500,5500,6600,7800,9100,
%T 10500,12000,13600,15300,17100,19000,21000,23100,25300,27600,30000,
%U 32500,35100,37800,40600,43500,46500,49600,52800,56100,59500,63000,66600
%N Experience Points thresholds for levels in the pen and paper role-playing game "Das Schwarze Auge" (DSA, a.k.a. "The Dark Eye").
%D "Das Schwarze Auge - Basisregelwerk" (basic rule book), Fantasy Productions Verlags- und Medienvertriebsgesellschaft mbH, Erkrath, Germany, 2005, ISBN 3890644406
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + (n-1)*100; a(1) = 0.
%F From _Chai Wah Wu_, Jul 11 2016: (Start)
%F a(n) = 50*n*(n-1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3.
%F G.f.: 100*x^2/(1 - x)^3. (End)
%e a(7)=2100 because a(6) + (7-1)*100 = (a(5) + 500) + 600 =(((((0+100) + 200) + 300) + 400) + 500) + 600.
%t Table[50 n (n - 1), {n, 37}] (* or *)
%t CoefficientList[Series[100 x^2/(1 - x)^3, {x, 0, 37}], x] (* _Michael De Vlieger_, Jul 11 2016 *)
%t LinearRecurrence[{3,-3,1},{0,100,300},40] (* _Harvey P. Dale_, Jun 26 2017 *)
%o (C) int folge(n){ if (n==1) return 0; return (folge(n-1)+(n-1)*100); }
%o (PARI) a(n)=50*n*(n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%K easy,nonn
%O 1,2
%A Christoph D. Schmidt (snu(AT)power.ms), Dec 16 2006, Dec 21 2006
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