A359620 Number of edge cuts in the n-antiprism graph.

1, 4, 62, 1440, 30346, 589556, 10858046, 192811016, 3336192082, 56642890908, 948242161382, 15706527467824, 258068117928826, 4214126476848580, 68489478048350222, 1109069751830483544, 17909240724783047842, 288575383662532867820, 4642173797092097149238

Offset: 0

Author

Eric W. Weisstein, Jan 07 2023

Keywords

• nonn

Comments

The n-antiprism graph is defined for n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Edge Cut
• Index entries for linear recurrences with constant coefficients, signature (42,-617,3640,-7144,5888,-2064,256).

Crossrefs

Cf. A359621.

Programs

Mathematica

Table[2 + 16^n - 2^(n + 1) ChebyshevT[n, 3] + (6 - 2^(n + 1) (Fibonacci[2 n, 2] + 3 Fibonacci[2 n - 1, 2])) n/7, {n, 10}] // Expand (* Eric W. Weisstein, Mar 07 2023 *)
LinearRecurrence[{42, -617, 3640, -7144, 5888, -2064, 256}, {1, 4, 62, 1440, 30346, 589556, 10858046}, 20] (* Eric W. Weisstein, Mar 07 2023 *)
CoefficientList[Series[-(1 - 38 x + 511 x^2 - 2336 x^3 + 704 x^4 + 512 x^5 + 16 x^6)/((-1 + x)^2 (-1 + 16 x) (1 - 12 x + 4 x^2)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

PARI

Vec((1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023

Formula

G.f.: (1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2). - Andrew Howroyd, Jan 26 2023

a(n) = 42*a(n-1) - 617*a(n-2) + 3640*a(n-3) - 7144*a(n-4) + 5888*a(n-5) - 2064*a(n-6) + 256*a(n-7). - Wesley Ivan Hurt, May 24 2024

Extensions

a(0)-(2) prepended and terms a(7) and beyond from Andrew Howroyd, Jan 26 2023