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A046524
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Number of coverings of Klein bottle with n lists.
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3
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1, 3, 2, 5, 2, 7, 2, 8, 3, 8, 2, 13, 2, 9, 4, 13, 2, 14, 2, 16, 4, 11, 2, 23, 3, 12, 4, 19, 2, 22, 2, 22, 4, 14, 4, 30, 2, 15, 4, 30, 2, 26, 2, 25, 6, 17, 2, 41, 3, 23, 4, 28, 2, 30, 4, 37, 4, 20, 2, 50, 2, 21, 6, 39, 4, 34, 2, 34, 4, 34, 2, 59, 2, 24, 6, 37, 4, 38, 2, 56, 5, 26, 2, 62, 4, 27, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| A. D. Mednykh, On the number of subgroups in the fundamental group of a closed surface. Commun. in Algebra, 16, No 10 (1988), 2137-2148.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
V. A. Liskovets and A. Mednykh, Number of non-orientable coverings of the Klein bottle
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FORMULA
| a(n)=d(n) (the number of divisors) for odd n.
a(n)=[3d(n)+sigma(n/2)-d(n/2)]/2 for even n where d(n) is the number and sigma(n) the sum of divisors of n (A00005 and A000203).
Inverse Moebius transform of 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, ... . G.f.: Sum_{n>1} x^n*(1+2*x^n-x^(4*n)-x^(5*n))/(1+x^(2*n))/(1-x^(2*n))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 03 2003
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MATHEMATICA
| kb[n_]:=If[OddQ[n], DivisorSigma[0, n], (3DivisorSigma[0, n]+ DivisorSigma[ 1, n/2]- DivisorSigma[0, n/2])/2]; Array[kb, 90] (* From Harvey P. Dale, Oct 08 2011 *)
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CROSSREFS
| Cf. A027842, A027844, A000005, A000203.
Sequence in context: A075410 A023513 A069735 * A105222 A086571 A133945
Adjacent sequences: A046521 A046522 A046523 * A046525 A046526 A046527
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KEYWORD
| nonn,easy,nice
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AUTHOR
| V. A. Liskovets (liskov(AT)im.bas-net.by)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 03 2003
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