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

2, 6, 152, 811008, 15502126646034432, 8348302506064411039310051552485442040121786368

Offset: 1

Author

Max Alekseyev, Sep 08 2014

Keywords

• nonn

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 Gasket Graph.

Crossrefs

Cf. A234635, A246957, A246959.

Programs

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 *)

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) ) )