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

%I A359620 #23 Feb 16 2025 08:34:04
%S A359620 1,4,62,1440,30346,589556,10858046,192811016,3336192082,56642890908,
%T A359620 948242161382,15706527467824,258068117928826,4214126476848580,
%U A359620 68489478048350222,1109069751830483544,17909240724783047842,288575383662532867820,4642173797092097149238
%N A359620 Number of edge cuts in the n-antiprism graph.
%C A359620 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
%H A359620 Andrew Howroyd, <a href="/A359620/b359620.txt">Table of n, a(n) for n = 0..200</a>
%H A359620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H A359620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>
%H A359620 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (42,-617,3640,-7144,5888,-2064,256).
%F A359620 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
%F A359620 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
%t A359620 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 *)
%t A359620 LinearRecurrence[{42, -617, 3640, -7144, 5888, -2064, 256}, {1, 4, 62, 1440, 30346, 589556, 10858046}, 20] (* _Eric W. Weisstein_, Mar 07 2023 *)
%t A359620 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 *)
%o A359620 (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
%Y A359620 Cf. A359621.
%K A359620 nonn
%O A359620 0,2
%A A359620 _Eric W. Weisstein_, Jan 07 2023
%E A359620 a(0)-(2) prepended and terms a(7) and beyond from _Andrew Howroyd_, Jan 26 2023