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Search: id:A138552
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| A138552 |
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Returning walks of length 2n on the upper half of the square lattice, distinct under reflections about the y-axis. |
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1
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| 1, 2, 11, 90, 889, 9723, 113322, 1380522, 17382365, 224573349, 2962117366, 39741658047, 540862505806, 7450655906450, 103713126384420, 1456845308244810, 20627719676855685, 294136002612344145
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Under reasonable assumptions, a(n)=E[X^{2n}] where the random variable X is the unitarized Frobenius trace X=a_p/sqrt(p) (as p varies) of a genus 2 curve whose Jacobian is isogenous to the product of two elliptic curves, exactly one of which has complex multiplication.
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REFERENCES
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Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials, and random matrices", preprint, 2008.
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FORMULA
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a(n)=(A000891(n)+A000108(n))/2
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EXAMPLE
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a(2) = 11 because EEWW, EWEW, EWWE, EWNS, ENSW, ENWS, NEWS, NESW, NSEW, NSNS, NNSS are all the walks of length 4 on the upper half of the square lattice that are distinct under reflections about the y-axis.
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CROSSREFS
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Cf. A000891.
Adjacent sequences: A138549 A138550 A138551 this_sequence A138553 A138554 A138555
Sequence in context: A106961 A099662 A099693 this_sequence A004677 A094955 A143870
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KEYWORD
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nonn
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AUTHOR
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Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 24 2008
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