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A098691 Array T(q,n) by antidiagonals: number of self-reciprocal polynomials of degree 2n over GF(q). 2
1, 1, 1, 2, 2, 1, 2, 4, 4, 2, 3, 6, 10, 10, 3, 3, 9, 20, 32, 24, 5, 4, 12, 35, 78, 102, 60, 9, 4, 16, 56, 162, 312, 340, 156, 16, 5, 20, 84, 300, 777, 1300, 1170, 410, 28, 5, 25, 120, 512, 1680, 3885, 5580, 4096, 1092, 51, 6, 30, 165, 820, 3276, 9800, 19995, 24414 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

Also, number of self-complementary necklaces of length n in q colors.

LINKS

Table of n, a(n) for n=2..64.

H. Meyn and W. Götz, Self-reciprocal polynomials over finite fields, Séminaire Lotharingien de Combinatoire, B21d (1989), 8 pp.

R. L. Miller, Necklaces, symmetries and self-reciprocal polynomials, Discr. Math. 22 (1978), 25-33.

FORMULA

(q^n-1)/2n for q odd and n=2^s; otherwise Sum[d|n, d odd, mu(d)*q^(n/d)] / 2n.

EXAMPLE

1,1,1,2,3,5,9,16,

1,2,4,10,24,60,156,410,

2,4,10,32,102,340,1170,4096,

2,6,20,78,312,1300,5580,24414,

3,9,35,162,777,3885,19995,104976,

3,12,56,300,1680,9800,58824,360300,

CROSSREFS

Rows include A000048. Columns 1-4 are A004526, A002620, A000292, 2*A011863. Main diagonal is in A098692.

Sequence in context: A261359 A217680 A144218 * A035364 A261734 A209308

Adjacent sequences:  A098688 A098689 A098690 * A098692 A098693 A098694

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Sep 21 2004

STATUS

approved

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Last modified February 23 15:43 EST 2018. Contains 299581 sequences. (Running on oeis4.)