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
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