A351587 Number of minimal edge covers in the n-cycle complement graph.
0, 1, 5, 25, 133, 859, 5781, 40923, 313005, 2541251, 21725314, 195840223, 1855631053, 18408258491, 190764140901, 2060930694871, 23161639995126, 270260975209117, 3268719600517612, 40914280736043141, 529233440391510248, 7065125832189189159, 97221637266999732570
Offset: 3
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 3..100
- Eric Weisstein's World of Mathematics, Cycle Complement Graph.
- Eric Weisstein's World of Mathematics, Minimal Edge Cover.
Programs
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PARI
a(n)={sum(i=0, n\2, sum(j=0, (n-2*i)\3, my(r=n-2*i-3*j, g=exp(x + O(x*x^r))); (-1)^i*n*((n-i-2*j-1)!/(i!*j!))*polcoef((2*g-1)^i*exp(j*x -x - x^2/2 + x*g), r)))} \\ Andrew Howroyd, Jun 14 2025
Formula
a(n) = Sum_{i=0..floor(n/2)} Sum{j=0..floor((n-2*i)/3)} (-1)^i * n * ((n-i-2*j-1)! / (i!*j!)) * [x^(n-2*i-3*j)] ((2*exp(x)-1)^i * exp(x)^j * exp(-x - x^2/2 + x*exp(x))). - Andrew Howroyd, Jun 14 2025
Extensions
a(9)-a(12) from Andrew Howroyd, Feb 21 2022
a(13) onwards from Andrew Howroyd, Jun 14 2025