A193256 - OEIS

%I #31 Feb 16 2025 08:33:15

%S 3,54,524880,803355125990400000,

%T 4800637927396055428150118355522551808000000000000000000

%N Number of spanning trees in the n-Sierpinski sieve graph.

%C a(7) = 1280086429813445... has 498 decimal digits.

%H Alois P. Heinz, <a href="/A193256/b193256.txt">Table of n, a(n) for n = 1..7</a>

%H E. Teufl and St. Wagner, <a href="http://mathinfo06.iecn.u-nancy.fr/papers/dmAG411-414.pdf">Spanning trees of finite Sierpinski graphs</a>, DMTCS proc. AG, 2006, 411-414

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiSieveGraph.html">Sierpinski Sieve Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>

%F a(n) = (3/20)^(1/4) * (5/3)^(-(n-1)/2) * (540^(1/4))^(3^(n-1)).

%p a:= proc(n) local t;

%p       t:= (3/20)^(1/4) * (5/3)^(-(n-1)/2) * (540^(1/4))^(3^(n-1));

%p       Digits:= 10 +ceil(log[10](t));

%p       round(t)

%p     end:

%p seq(a(n), n=1..8);

%t Table[2^(1/6 (-3 + 3^n)) 3^(1/4 (-1 + 3^n + 2 n)) 5^(1/12 (3 + 3^n - 6 n)), {n, 8}] (* _Eric W. Weisstein_, Jun 17 2017 *)

%K nonn,changed

%O 1,1

%A _Alois P. Heinz_, Jul 19 2011