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A002348
Degree of rational Poncelet porism of n-gon.
(Formerly M0549 N0198)
2
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
OFFSET
3,2
REFERENCES
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).
LINKS
Eric Weisstein's World of Mathematics, Poncelet's Porism
EXAMPLE
For a triangle the degree is 1, thus a(3) = 1. - Michael Somos, Dec 07 2018
MATHEMATICA
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 ] ]
PROG
(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
-- Reinhard Zumkeller, Mar 18 2012
CROSSREFS
Sequence in context: A097273 A006446 A261342 * A019469 A081491 A048716
KEYWORD
nonn,nice
EXTENSIONS
Extended with Mathematica program by Eric W. Weisstein
STATUS
approved