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A196081
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Dungeons and Dragons Ability Modifier Sequence.
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1
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10, 0, 11, 0, 12, 1, 13, 1, 14, 2, 15, 2, 16, 3, 17, 3, 18, 4, 19, 4, 20, 5, 21, 5, 22, 6, 23, 6, 24, 7, 25, 7, 26, 8, 27, 8, 28, 9, 29, 9, 30, 10, 31, 10, 32, 11, 33, 11, 34, 12, 35
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refs;
listen;
history;
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OFFSET
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0,1
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REFERENCES
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Rob Heinsoo and Andy Collins and James Wyatt, Wizards of the Coast, 2008, page 17, Dungeons and Dragons Player's Handbook
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..999
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).
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FORMULA
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a(n+5) = a(n)+a(n+1)-a(n+4)+3. - Alexander R. Povolotsky, Sep 27 2011
a(n) = 19/4-(1/8*I)*I^n+1/8*(-1)^n*n+21/4*(-1)^n+3/8*n+(1/8*I)*(-I)^n. - Alexander R. Povolotsky, Sep 27 2011
G.f.: ( 10+x^2-9*x^4+x^5 ) / ( (x^2+1)*(x-1)^2*(1+x)^2 ). - R. J. Mathar, Sep 27 2011
a(2n) = n+10.
a(2n+1) = A004526(n).
a(0)=10, a(1)=0, a(2)=11, a(3)=0, a(4)=12, a(5)=1, a(n)=a(n-2)+a(n-4)- a(n-6). - Harvey P. Dale, Oct 01 2011
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MATHEMATICA
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LinearRecurrence[{0, 1, 0, 1, 0, -1}, {10, 0, 11, 0, 12, 1}, 60] (* or *) CoefficientList[Series[(10+x^2-9x^4+x^5)/((x^2+1)(x-1)^2(1+x)^2), {x, 0, 60}], x] (* Harvey P. Dale, Oct 01 2011 *)
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PROG
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(C#)
public int Modifier(int score) {int modifier = 0; if (score % 2 == 0) {modifier = score / 2 - 5; } else {modifier = (score -1) / 2 - 5; } return modifier; }
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CROSSREFS
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Sequence in context: A095418 A055961 A341504 * A320380 A088001 A344071
Adjacent sequences: A196078 A196079 A196080 * A196082 A196083 A196084
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KEYWORD
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nonn,easy
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AUTHOR
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Daniel Ray, Sep 27 2011
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STATUS
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approved
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