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 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 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

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