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A085624 Sum of the entries in the character table of the dihedral group D_{2n} of order 2n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

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 A345426 A061884

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

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)