cp's OEIS Frontend

A085624 Sum of the entries in the character table of the dihedral group D_{2n} of order 2n.

%I A085624 #26 Jun 14 2024 11:35:58
%S A085624 2,4,5,8,8,10,11,14,14,16,17,20,20,22,23,26,26,28,29,32,32,34,35,38,
%T A085624 38,40,41,44,44,46,47,50,50,52,53,56,56,58,59,62,62,64,65,68,68,70,71,
%U A085624 74,74,76,77,80,80,82,83,86,86,88,89,92,92,94,95,98,98,100
%N A085624 Sum of the entries in the character table of the dihedral group D_{2n} of order 2n.
%H A085624 Eric M. Schmidt, <a href="/A085624/b085624.txt">Table of n, a(n) for n = 1..1000</a>
%H A085624 Arvind Ayyer, Hiranya Kishore Dey, and Digjoy Paul, <a href="https://arxiv.org/abs/2406.06036">How large is the character degree sum compared to the character table sum for a finite group?</a>, arXiv:2406.06036 [math.RT], 2024. See p. 4.
%H A085624 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A085624 From _Eric M. Schmidt_, Jul 08 2012: (Start)
%F A085624 If n is odd, a(n) = (3n + 1)/2.
%F A085624 If n == 2 (mod 4), a(n) = (3n + 2)/2.
%F A085624 If 4 divides n, a(n) = (3n + 4)/2. (End)
%F A085624 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
%F A085624 a(n) = 1+(6*n+(1+(-1)^n)*i^n+2*(-1)^n)/4, where i=sqrt(-1). - _Bruno Berselli_, Jul 09 2012
%e A085624 The character table for D_8 is
%e A085624  1  1  1  1  1
%e A085624  1  1  1 -1 -1
%e A085624  1  1 -1  1 -1
%e A085624  1  1 -1 -1  1
%e A085624  2 -2  0  0  0
%t A085624 Table[1 + (6 n + (1 + (-1)^n) I^n + 2 (-1)^n)/4, {n, 66}] (* _Bruno Berselli_, Jul 09 2012 *)
%t A085624 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 *)
%o A085624 (GAP) Display(CharacterTable("D8"));
%o A085624 (Maxima) makelist(1+(6*n+(1+(-1)^n)*%i^n+2*(-1)^n)/4,n,1,66); /* _Bruno Berselli_, Jul 09 2012 */
%K A085624 nonn,easy
%O A085624 1,1
%A A085624 Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 09 2003
%E A085624 More terms from _Eric M. Schmidt_, Jul 08 2012