A246958 Number of directed Hamiltonian paths in the n-Sierpiński sieve graph that starts at the fixed corner.

2, 6, 152, 811008, 15502126646034432, 8348302506064411039310051552485442040121786368

Offset

1,1

Comments

Explicit formula and asymptotic are given by Chang and Chen (2011).

a(7) contains 134 decimal digits.

Links

Table of n, a(n) for n=1..6.

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

Cf. A234635, A246957, A246959.

Sequence in context: A015173 A122570 A088430 * A219761 A051240 A003189

Adjacent sequences: A246955 A246956 A246957 * A246959 A246960 A246961

Keyword

nonn

Author

Max Alekseyev, Sep 08 2014

Status

approved