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A132102
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Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.
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4
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1, 1, 3, 7, 35, 193, 1799, 19311, 254143, 3828921, 65486307, 1249937335, 26353147811, 608142583137, 15247011443103, 412685556939751, 11993674252049647, 372509404162520641, 12313505313357313047, 431620764875678503143, 15991549339008732109899
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OFFSET
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0,3
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COMMENTS
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Turning over is not allowed.
See A132100 for definition and comments.
Even and odd terms can be computed with the help of Burnside Lemma and recursive sequences. - Lionel RAVEL, Sep 18 2013
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) = (1/n)*Sum_{d|n} phi(d)*alpha(d, n/d), where phi = Euler's totient function,
alpha(p,q) = Sum_{j=0..q} p^j * binomial(2q, 2j) * (2j-1)!! if p even,
= p^q * (2q-1)!! if p odd. (cf. also A132100) - Laurent Tournier, Jul 09 2014
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MAPLE
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with(numtheory): a:=(p, q)->piecewise(p mod 2 = 1, p^q*doublefactorial(2*q - 1), sum(p^j*binomial(2*q, 2*j)*doublefactorial(2*j - 1), j = 0 .. q));
A132102 := n->add(phi(p)*a(p, n/p), p in divisors(n))/n;
[seq(A132102(n), n=1..20)]; # Laurent Tournier, Jul 09 2014
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PROG
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(PARI) a(n)={if(n<1, n==0, sumdiv(n, d, my(m=n/d); eulerphi(d)*sum(j=0, m, (d%2==0 || m-j==0) * binomial(2*m, 2*j) * d^j * (2*j)! / (j!*2^j) ))/n)} \\ Andrew Howroyd, Jan 26 2020
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CROSSREFS
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Cf. A001147, A007769, A054499, A132100, A132101, A132103, A132104, A132105.
Sequence in context: A053530 A215575 A266049 * A081555 A301341 A063042
Adjacent sequences: A132099 A132100 A132101 * A132103 A132104 A132105
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KEYWORD
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nonn
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AUTHOR
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Keith F. Lynch, Oct 31 2007
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EXTENSIONS
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More terms from Lionel RAVEL, Sep 18 2013
a(9) and a(10) corrected, and addition of more terms using formula given above by Laurent Tournier, Jul 09 2014
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STATUS
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approved
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