A085624 Sum of the entries in the character table of the dihedral group D_{2n} of order 2n.
2, 4, 5, 8, 8, 10, 11, 14, 14, 16, 17, 20, 20, 22, 23, 26, 26, 28, 29, 32, 32, 34, 35, 38, 38, 40, 41, 44, 44, 46, 47, 50, 50, 52, 53, 56, 56, 58, 59, 62, 62, 64, 65, 68, 68, 70, 71, 74, 74, 76, 77, 80, 80, 82, 83, 86, 86, 88, 89, 92, 92, 94, 95, 98, 98, 100
Offset: 1
Examples
The character table for D_8 is 1 1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 2 -2 0 0 0
Links
- Eric M. Schmidt, Table of n, a(n) for n = 1..1000
- Arvind Ayyer, Hiranya Kishore Dey, and Digjoy Paul, How large is the character degree sum compared to the character table sum for a finite group?, arXiv:2406.06036 [math.RT], 2024. See p. 4.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
-
GAP
Display(CharacterTable("D8")); -
Mathematica
Table[1 + (6 n + (1 + (-1)^n) I^n + 2 (-1)^n)/4, {n, 66}] (* Bruno Berselli, Jul 09 2012 *) Table[Which[OddQ[n],(3n+1)/2,Mod[n,4]==2,(3n+2)/2,Mod[n,4]==0,(3n+4)/2],{n,70}] (* Harvey P. Dale, Mar 06 2020 *) -
Maxima
makelist(1+(6*n+(1+(-1)^n)*%i^n+2*(-1)^n)/4,n,1,66); /* Bruno Berselli, Jul 09 2012 */
Formula
From Eric M. Schmidt, Jul 08 2012: (Start)
If n is odd, a(n) = (3n + 1)/2.
If n == 2 (mod 4), a(n) = (3n + 2)/2.
If 4 divides n, a(n) = (3n + 4)/2. (End)
G.f.: x*(2+2*x+x^2+3*x^3-2*x^4)/((1-x)^2*(1+x+x^2+x^3)). - Bruno Berselli, Jul 09 2012
a(n) = 1+(6*n+(1+(-1)^n)*i^n+2*(-1)^n)/4, where i=sqrt(-1). - Bruno Berselli, Jul 09 2012
Extensions
More terms from Eric M. Schmidt, Jul 08 2012