%I #16 Feb 16 2025 08:33:23
%S 2,6,152,811008,15502126646034432,
%T 8348302506064411039310051552485442040121786368
%N Number of directed Hamiltonian paths in the n-Sierpiński sieve graph that starts at the fixed corner.
%C Explicit formula and asymptotic are given by Chang and Chen (2011).
%C a(7) contains 134 decimal digits.
%H S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:<a href="http://dx.doi.org/10.1063/1.3545358">10.1063/1.3545358</a>. See <a href="http://arxiv.org/abs/0909.5541">also</a>, arXiv:0909.5541 [cond-mat.stat-mech], 2009.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiSieveGraph.html">Sierpiński Sieve Graph</a>
%t 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])];
%t Array[a, 6] (* _Jean-François Alcover_, Dec 04 2018, from PARI *)
%o (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) ) )
%Y Cf. A234635, A246957, A246959.
%K nonn,changed
%O 1,1
%A _Max Alekseyev_, Sep 08 2014