A234635 -id:A234635 - cp's OEIS frontend

A246959 Numbers of (undirected) Hamiltonian cycles in the n-Sierpiński gasket graph.

1, 1, 8, 13824, 71328803586048, 9798477119793909670551703700100284084649984

Offset: 1

Max Alekseyev, Sep 08 2014

nonn

R. M. Bradley, Statistical mechanics of the travelling salesman on the Sierpinski gasket, J. Physique, 47 (1986), 9-14. doi:10.1051/jphys:019860047010900.
S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:10.1063/1.3545358. arXiv:0909.5541.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle.
Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.

[1,1] cat [Floor(8 * 12^((3^(n-2)-3)/2)): n in [3..10]]; // Vincenzo Librandi, Jun 15 2015

Join[{1, 1}, Table[8 12^((3^(n - 2) - 3)/2), {n, 3, 8}]] (* Eric W. Weisstein, Jun 17 2017 *)
Join[{1, 1}, RecurrenceTable[{a[3] == 8, a[n] == (3 a[n - 1])^3}, a, {n, 3, 8}]] (* Eric W. Weisstein, Mar 25 2018 *)

For n >= 3, a(n) = 8 * 12^((3^(n-2)-3)/2).

For n >= 4, a(n) = (3*a(n-1))^3.

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

Original entry on oeis.org

2, 6, 152, 811008, 15502126646034432, 8348302506064411039310051552485442040121786368

Offset: 1

Max Alekseyev, Sep 08 2014

nonn

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

a(7) contains 134 decimal digits.

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.

Cf. A234635, A246957, A246959.

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 *)

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) ) )

A246957 Numbers of (undirected) Hamiltonian paths in the n-Sierpiński gasket graph.

Original entry on oeis.org

3, 12, 552, 6978816, 429714433137180672, 868161947968780041877535786874146453722578812928

Offset: 1

Max Alekseyev, Sep 08 2014

nonn

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

a(7) contains 137 decimal digits.

S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:10.1063/1.3545358. arXiv:0909.5541.
Eric Weisstein's World of Mathematics, Hamiltonian Path.
Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.

Cf. A234635, A246958, A246959.

A288629 Number of (undirected) paths in the n-Sierpinski gasket graph.

Original entry on oeis.org

6, 108, 49194, 328040263752, 3114828284506941483786172285326

Offset: 1

Eric W. Weisstein, Jun 17 2017

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..7
Eric Weisstein's World of Mathematics, Graph Path.
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Cf. A234634, A234635.

a(4) onwards from Andrew Howroyd, Aug 08 2024

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A246959 Numbers of (undirected) Hamiltonian cycles in the n-Sierpiński gasket graph.

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

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A246957 Numbers of (undirected) Hamiltonian paths in the n-Sierpiński gasket graph.

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A288629 Number of (undirected) paths in the n-Sierpinski gasket graph.

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