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A098691
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Array T(q,n) by antidiagonals: number of self-reciprocal polynomials of degree 2n over GF(q).
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2
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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; internal format)
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OFFSET
| 2,4
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COMMENTS
| Also, number of self-complementary necklaces of length n in q colors.
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REFERENCES
| R. L. Miller, Necklaces, symmetries and self-reciprocal polynomials, Discr. Math. 22 (1978), 25-33.
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LINKS
| H. Meyn and W. G\"otz, Self-reciprocal polynomials over finite fields
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FORMULA
| (q^n-1)/2n for q odd and n=2^s; otherwise Sum[d|n, d odd, mu(d)*q^(n/d)] / 2n.
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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,
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CROSSREFS
| Rows include A000048. Columns 1-4 are A004526, A002620, A000292, 2*A011863. Main diagonal is in A098692.
Sequence in context: A035374 A048299 A144218 * A035364 A143808 A172021
Adjacent sequences: A098688 A098689 A098690 * A098692 A098693 A098694
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Sep 21 2004
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