A292076 Number of 4-cycles in the n-Menger sponge graph.
0, 192, 5952, 137664, 2907456, 59398080, 1197999936, 24040445376, 481452900672, 9634211218368, 192725453785920, 3854838922404288, 77099417255585088, 1542009455673733056, 30840357998277021504, 616808511044877643200, 12336181029535005559104, 246723707059807997713344
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Graph Cycle.
- Eric Weisstein's World of Mathematics, Menger Sponge Graph.
- Index entries for linear recurrences with constant coefficients, signature (31,-244,480).
Programs
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PARI
a(n) = 16*(5*20^n - 17*8^n + 12*3^n)/85 \\ Andrew Howroyd, Jun 12 2025
Formula
From Andrew Howroyd, Jun 12 2025: (Start)
a(n) = Sum_{k=1..n-1} 8*3^(k-1)*A291066(n-k).
a(n) = 16*(5*20^n - 17*8^n + 12*3^n)/85. (End)
Extensions
a(7) onwards from Andrew Howroyd, Jun 12 2025