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A359622 Number of edge cuts in the n-Moebius ladder.

%I A359622 #14 Feb 16 2025 08:34:04
%S A359622 1,26,307,3004,27049,232658,1947103,16021784,130447957,1055068574,
%T A359622 8498016971,68269451044,547562782017,4387403277994,35132904838583,
%U A359622 281226897433648,2250607478637613,18008682685966262,144087851840540835,1152791046751807804,9222750661998396185,73784021962658308290
%N A359622 Number of edge cuts in the n-Moebius ladder.
%H A359622 Andrew Howroyd, <a href="/A359622/b359622.txt">Table of n, a(n) for n = 1..200</a>
%H A359622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>
%H A359622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H A359622 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (20,-146,488,-777,612,-228,32).
%F A359622 G.f.: x*(1 + 6*x - 67*x^2 + 172*x^3 - 120*x^4 + 36*x^5)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2). - _Andrew Howroyd_, Jan 26 2023
%t A359622 Table[With[{a = 5 - Sqrt[17], b = 5 + Sqrt[17]}, 1 + 8^n - n - ((n + 2) (a^n + b^n) - n (b^n - a^n)/Sqrt[17])/2^(n + 1)], {n, 20}] // Expand (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A359622 LinearRecurrence[{20, -146, 488, -777, 612, -228, 32}, {1, 26, 307, 3004, 27049, 232658, 1947103}, 20] (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A359622 CoefficientList[Series[-(1 + 6 x - 67 x^2 + 172 x^3 - 120 x^4 + 36 x^5)/((-1 + x)^2 (-1 + 8 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Dec 01 2024 *)
%o A359622 (PARI) Vec((1 + 6*x - 67*x^2 + 172*x^3 - 120*x^4 + 36*x^5)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2) + O(x^20)) \\ _Andrew Howroyd_, Jan 26 2023
%K A359622 nonn,easy
%O A359622 1,2
%A A359622 _Eric W. Weisstein_, Jan 07 2023
%E A359622 a(1)-a(2) prepended and terms a(8) and beyond from _Andrew Howroyd_, Jan 26 2023