A378922 Number of minimal edge cuts in the n-antiprism graph.
1, 1, 7, 28, 81, 191, 391, 722, 1233, 1981, 3031, 4456, 6337, 8763, 11831, 15646, 20321, 25977, 32743, 40756, 50161, 61111, 73767, 88298, 104881, 123701, 144951, 168832, 195553, 225331, 258391, 294966, 335297, 379633, 428231, 481356, 539281, 602287, 670663, 744706, 824721
Offset: 0
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Eric Weisstein's World of Mathematics, Antiprism Graph.
- Eric Weisstein's World of Mathematics, Minimal Edge Cut.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A359620.
Programs
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PARI
a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6 \\ Andrew Howroyd, Jun 09 2025
Formula
From Andrew Howroyd, Jun 09 2025: (Start)
a(n) = 1 + 2*n*(n-1) + n^2*(n-1)*(2*n-1)/6.
a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6. (End)
From Elmo R. Oliveira, Sep 03 2025: (Start)
G.f.: (1 - 4*x + 12*x^2 - 7*x^3 + 6*x^4)/(1-x)^5.
E.g.f.: (6 + 18*x^2 + 9*x^3 + 2*x^4)*exp(x)/6.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)
Extensions
a(0)-a(2) prepended and a(7) onwards from Andrew Howroyd, Jun 09 2025
Comments