A124437 Experience Points thresholds for levels in the pen and paper role-playing game "Das Schwarze Auge" (DSA, a.k.a. "The Dark Eye").

0, 100, 300, 600, 1000, 1500, 2100, 2800, 3600, 4500, 5500, 6600, 7800, 9100, 10500, 12000, 13600, 15300, 17100, 19000, 21000, 23100, 25300, 27600, 30000, 32500, 35100, 37800, 40600, 43500, 46500, 49600, 52800, 56100, 59500, 63000, 66600

Offset: 1

Author

Christoph D. Schmidt (snu(AT)power.ms), Dec 16 2006, Dec 21 2006

Keywords

• easy
• nonn

Examples

			a(7)=2100 because a(6) + (7-1)*100 = (a(5) + 500) + 600 =(((((0+100) + 200) + 300) + 400) + 500) + 600.
		

References

• "Das Schwarze Auge - Basisregelwerk" (basic rule book), Fantasy Productions Verlags- und Medienvertriebsgesellschaft mbH, Erkrath, Germany, 2005, ISBN 3890644406

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

C

int folge(n){ if (n==1) return 0; return (folge(n-1)+(n-1)*100); }

Mathematica

Table[50 n (n - 1), {n, 37}] (* or *)
CoefficientList[Series[100 x^2/(1 - x)^3, {x, 0, 37}], x] (* Michael De Vlieger, Jul 11 2016 *)
LinearRecurrence[{3,-3,1},{0,100,300},40] (* Harvey P. Dale, Jun 26 2017 *)

PARI

a(n)=50*n*(n-1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = a(n-1) + (n-1)*100; a(1) = 0.

From Chai Wah Wu, Jul 11 2016: (Start)

a(n) = 50*n*(n-1).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3.

G.f.: 100*x^2/(1 - x)^3. (End)