A246957 -id:A246957 - 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) ) )

A234635 Numbers of directed Hamiltonian paths in the n-Sierpinski gasket graph.

Original entry on oeis.org

6, 24, 1104, 13957632, 859428866274361344, 1736323895937560083755071573748292907445157625856

Offset: 1

Eric W. Weisstein, Dec 28 2013

nonn

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

a(7) contains 137 decimal digits.

Eric Weisstein's World of Mathematics, Hamiltonian Path.
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.
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

Cf. A246957, A246958, A246959.

a(n) = A246957(n)*2.

a(5)-a(6) added by Max Alekseyev, Sep 08 2014

A234634 Numbers of undirected cycles in the n-Sierpinski gasket graph.

Original entry on oeis.org

1, 11, 1033, 1030304099, 873851166316875626844153297, 531723201747806346628696993678355296791302025810590916630277786972117723914960891

Offset: 1

Eric W. Weisstein, Dec 28 2013

nonn

Term a(7) has 243 decimal digits and a(8) has 727 decimal digits. - Andrew Howroyd, Jun 18 2017

Andrew Howroyd, Table of n, a(n) for n = 1..8
Eric Weisstein's World of Mathematics, Graph Cycle.
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Cf. A246957, A246958, A246959.

a(4)-a(6) from Andrew Howroyd, Jun 18 2017

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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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A234635 Numbers of directed Hamiltonian paths in the n-Sierpinski gasket graph.

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A234634 Numbers of undirected cycles in the n-Sierpinski gasket graph.

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