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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
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
1,2
REFERENCES
"Das Schwarze Auge - Basisregelwerk" (basic rule book), Fantasy Productions Verlags- und Medienvertriebsgesellschaft mbH, Erkrath, Germany, 2005, ISBN 3890644406
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)
EXAMPLE
a(7)=2100 because a(6) + (7-1)*100 = (a(5) + 500) + 600 =(((((0+100) + 200) + 300) + 400) + 500) + 600.
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 *)
PROG
(C) int folge(n){ if (n==1) return 0; return (folge(n-1)+(n-1)*100); }
(PARI) a(n)=50*n*(n-1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A261276 A104908 A109633 * A349181 A138668 A017174
KEYWORD
easy,nonn
AUTHOR
Christoph D. Schmidt (snu(AT)power.ms), Dec 16 2006, Dec 21 2006
STATUS
approved