A377771 Number of edge cuts in the n-trapezohedral graph.

1, 13, 185, 3013, 51009, 864453, 14514449, 241137749, 3969473217, 64867543333, 1054153461745, 17059836799733, 275240835803937, 4430702562116805, 71206049773837905, 1142980976834497173, 18330756374528899457, 293794963549100393573, 4706588394482611291313, 75373885078381735479861

Offset: 0

Author

Eric W. Weisstein, Nov 06 2024

Keywords

• nonn
• easy
• changed

Comments

The sequence has been extended to n = 0 using the recurrence. - Andrew Howroyd, Dec 19 2024

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Edge Cut.
• Eric Weisstein's World of Mathematics, Trapezohedral Graph.
• Index entries for linear recurrences with constant coefficients, signature (39,-531,2997,-6588,5956,-2128,256).

Crossrefs

Cf. A356213.

Programs

Mathematica

Table[16^n - 1 - 2^(n + 1) ChebyshevT[n, 3] + RootSum[-4 + 17 # - 10 #^2 + #^3 &, #^n &], {n, 0, 20}] (* Eric W. Weisstein, Sep 06 2025 *)
LinearRecurrence[{39, -531, 2997, -6588, 5956, -2128, 256}, {3013, 51009, 864453, 14514449, 241137749, 3969473217, 64867543333}, {-2, 20}] (* Eric W. Weisstein, Sep 06 2025 *)
CoefficientList[Series[-(1 - 26 x + 209 x^2 - 296 x^3 - 636 x^4 + 248 x^5 + 80 x^6)/((-1 + x) (-1 + 16 x) (1 - 12 x + 4 x^2) (-1 + 10 x - 17 x^2 + 4 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 06 2025 *)

PARI

Vec((1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)) + O(x^21)) \\ Andrew Howroyd, Dec 19 2024

Formula

G.f.: (1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)). - Andrew Howroyd, Dec 19 2024

a(n) = 39*a(n-1)-531*a(n-2)+2997*a(n-3)-6588*a(n-4)+5956*a(n-5)-2128*a(n-6)+256*a(n-7). - Eric W. Weisstein, Sep 06 2025

Extensions

a(0)-a(2) prepended and a(7) onwards from Andrew Howroyd, Dec 19 2024