|
| |
|
|
A007147
|
|
Number of self-dual 2-colored necklaces with 2n beads.
(Formerly M0319)
|
|
2
| |
|
|
1, 1, 2, 2, 4, 5, 9, 12, 23, 34, 63, 102, 190, 325, 612, 1088, 2056, 3771, 7155, 13364, 25482, 48175, 92205, 175792, 337594, 647326, 1246863, 2400842, 4636390, 8956060, 17334801, 33570816, 65108062, 126355336, 245492244, 477284182
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| E. M. Palmer and R. W. Robinson, Enumeration of self-dual configurations, Pacific J. Math., 110 (1984), 203-221.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| Index entries for sequences related to necklaces
|
|
|
MATHEMATICA
| a[n_] := (1/2)*(2^Quotient[n-1, 2] + Total[(Mod[#, 2]*EulerPhi[#]*2^(n/#) & ) /@ Divisors[n]]/(2*n)); Table[a[n], {n, 1, 36}] (* From Jean-François Alcover, Oct 24 2011, after Pari *)
|
|
|
PROG
| (PARI) a(n)= (1/2) *(2^((n-1)\2)+sumdiv(n, k, (k%2)*eulerphi(k)*2^(n/k))/(2*n))
|
|
|
CROSSREFS
| Cf. A000016, A016116. a(n)= (1/2) *(A016116(n-1)+A000016(n)).
Sequence in context: A102526 A050192 A191786 * A127968 A188541 A037026
Adjacent sequences: A007144 A007145 A007146 * A007148 A007149 A007150
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Michael Somos
|
| |
|
|
