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A002348
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Degree of rational Poncelet porism of n-gon.
(Formerly M0549 N0198)
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2
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1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 21, 24, 24, 32, 36, 36, 45, 48, 48, 60, 66, 64, 75, 84, 81, 96, 105, 96, 120, 128, 120, 144, 144, 144, 171, 180, 168, 192, 210, 192, 231, 240, 216, 264, 276, 256, 294, 300, 288, 336, 351, 324, 360, 384, 360, 420, 435, 384, 465
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OFFSET
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3,2
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REFERENCES
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Kerawala, S. M.; Poncelet Porism in Two Circles. Bull. Calcutta Math. Soc. 39, 85-105, 1947.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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For a triangle the degree is 1, thus a(3) = 1. - Michael Somos, Dec 07 2018
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MATHEMATICA
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Poncelet[ n_Integer /; n >= 3 ] := Module[ {p, a, i}, {p, a}=Transpose[ FactorInteger[ n ] ];
If[ p[[1]]==2, 4^a[[1]] Product[ p[[i]]^(2(a[[i]] - 1))(p[[i]]^2 - 1), {i, 2, Length[ p ]} ]/8, (* Else *) Product[ p[[i]]^(2(a[[i]] - 1))(p[[i]]^2 - 1), {i, Length[ p ]} ]/8 ] ]
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PROG
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(PARI) {a(n) = my(p, e); if( n<3, 0, p=factor(n)~; e=p[2, ]; p=p[1, ]; if( p[1]==2, 4^e[1], 1) * prod(i=1 + (p[1]==2), length(p), p[i]^(2*(e[i] - 1)) * (p[i]^2 - 1)) / 8)}; /* Michael Somos, Dec 09 1999 */
(Haskell)
a002348 n = product (zipWith d ps es) * 4 ^ e0 `div` 8 where
d p e = (p ^ 2 - 1) * p ^ e
e0 = if even n then head $ a124010_row n else 0
es = map ((* 2) . subtract 1) $
if even n then tail $ a124010_row n else a124010_row n
ps = if even n then tail $ a027748_row n else a027748_row n
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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