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

1,1

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).

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

Example

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

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 *)

Prog

(GAP) Display(CharacterTable("D8"));
(Maxima) makelist(1+(6*n+(1+(-1)^n)*%i^n+2*(-1)^n)/4, n, 1, 66); /* Bruno Berselli, Jul 09 2012 */

Crossrefs

Sequence in context: A088580 A036699 A036694 * A331376 A369601 A345426

Adjacent sequences: A085621 A085622 A085623 * A085625 A085626 A085627

Keyword

nonn,easy

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 09 2003

Extensions

More terms from Eric M. Schmidt, Jul 08 2012

Status

approved