A308155 Number of (undirected) cycles in the n-Hanoi graph.

1, 11, 1761, 6560212131, 282779810128722710004851715561, 22612323802416302740572466532825193607455652273991093701620185148186749274755003474250171

Offset

1,2

Comments

a(7) has 266 decimal digits and a(8) has 796 decimal digits. - Andrew Howroyd, Sep 10 2019

Also the number of chordless cycles in the (n+1)-Hanoi graph. - Eric W. Weisstein, May 23 2023

Links

Andrew Howroyd, Table of n, a(n) for n = 1..8

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Hanoi Graph

Formula

a(n) = Sum_{k=1..n} 3^(n-k)*A125295(k-1)^3. - Andrew Howroyd, Sep 10 2019

Mathematica

a[0] = 1; a[n_] := a[n] = a[n - 1]^2 (a[n - 1] + 1); Table[Sum[3^(n - k) a[k - 1]^3, {k, n}], {n, 6}] (* Eric W. Weisstein, May 23 2023 *)

Prog

(PARI) a(n)={my(s=1, d=1); for(i=2, n, d=d^2+d^3; s = 3*s + d^3); s} \\ Andrew Howroyd, Sep 10 2019

Crossrefs

Cf. A125295, A288796, A308134.

Sequence in context: A222841 A287035 A297004 * A222874 A028453 A024151

Adjacent sequences: A308152 A308153 A308154 * A308156 A308157 A308158

Keyword

nonn

Author

Eric W. Weisstein, May 14 2019

Extensions

a(4)-a(6) from Andrew Howroyd, Sep 10 2019

Status

approved