|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
_Reinhard Zumkeller_, Table of n, a(n) for n = 3..10000
Eric Weisstein's World of Mathematics, Poncelet's Porism
|
|
|
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)= local(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
|
Cf. A027748, A124010.
Sequence in context: A033501 A097273 A006446 * A019469 A081491 A048716
Adjacent sequences: A002345 A002346 A002347 * A002349 A002350 A002351
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
Extended with Mathematica program by Eric W. Weisstein
|
|
|
STATUS
|
approved
|
| |
|
|
