A196081 Dungeons and Dragons Ability Modifier Sequence.

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

Offset

0,1

References

Rob Heinsoo and Andy Collins and James Wyatt, Wizards of the Coast, 2008, page 17, Dungeons and Dragons Player's Handbook

Links

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).

Formula

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

Mathematica

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 *)

Prog

(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; }

Crossrefs

Sequence in context: A095418 A055961 A341504 * A320380 A088001 A344071

Adjacent sequences: A196078 A196079 A196080 * A196082 A196083 A196084

Keyword

nonn,easy

Author

Daniel Ray, Sep 27 2011

Status

approved