The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246958 Number of directed Hamiltonian paths in the n-Sierpiński sieve graph that starts at the fixed corner. 5
2, 6, 152, 811008, 15502126646034432, 8348302506064411039310051552485442040121786368 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Explicit formula and asymptotic are given by Chang and Chen (2011).
a(7) contains 134 decimal digits.
LINKS
S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:10.1063/1.3545358. See also, arXiv:0909.5541 [cond-mat.stat-mech], 2009.
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Sierpiński Sieve Graph
MATHEMATICA
a[n_] := Module[{m}, If[n == 1, Return[2]]; m = 3^(n-2); 2^m*3^((m-1)/2)* (7*17/(2^4*3^3)*4^(n-1) + 2^2*13/3^3 - If[n == 2, 1/(2^2*3^2), 0])];
Array[a, 6] (* Jean-François Alcover, Dec 04 2018, from PARI *)
PROG
(PARI) A246958(n) = if(n==1, return(2)); my(m=3^(n-2)); 2^m * 3^((m-1)/2) * ( 7*17/(2^4*3^3)*4^(n-1) + 2^2*13/(3^3) - if(n==2, 1/(2^2*3^2) ) )
CROSSREFS
Sequence in context: A015173 A122570 A088430 * A219761 A051240 A003189
KEYWORD
nonn
AUTHOR
Max Alekseyev, Sep 08 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 14:30 EDT 2024. Contains 372630 sequences. (Running on oeis4.)