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A085624
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Sum of the entries in the character table of the dihedral group D_{2n} of order 2n.
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2
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 09 2003
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EXTENSIONS
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STATUS
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approved
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