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A359621 Number of edge cuts in the n-prism graph.

%I A359621 #13 Feb 16 2025 08:34:04
%S A359621 1,4,31,314,3013,27060,232671,1947118,16021801,130447976,1055068595,
%T A359621 8498016994,68269451069,547562782044,4387403278023,35132904838614,
%U A359621 281226897433681,2250607478637648,18008682685966299,144087851840540874,1152791046751807845
%N A359621 Number of edge cuts in the n-prism graph.
%C A359621 The n-prism graph is defined from n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - _Andrew Howroyd_, Jan 26 2023
%H A359621 Andrew Howroyd, <a href="/A359621/b359621.txt">Table of n, a(n) for n = 0..200</a>
%H A359621 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>
%H A359621 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A359621 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (20, -146, 488, -777, 612, -228, 32).
%F A359621 G.f.: (1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2). - _Andrew Howroyd_, Jan 26 2023
%F A359621 a(n) = 20*a(n-1)-146*a(n-2)+488*a(n-3)-777*a(n-4)+612*a(n-5)-228*a(n-6)+32*a(n-7). - _Eric W. Weisstein_, Dec 01 2024
%t A359621 Table[2 + 8^n + n + (((17^(-1/2) - 1) n - 2) (5 + Sqrt[17])^n - ((17^(-1/2) + 1) n + 2) (5 - Sqrt[17])^n)/2^(n + 1), {n, 0, 20}] // Expand (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A359621 LinearRecurrence[{20, -146, 488, -777, 612, -228, 32}, {1, 4, 31, 314, 3013, 27060, 232671}, 20] (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A359621 CoefficientList[Series[-(1 - 16 x + 97 x^2 - 210 x^3 + 84 x^4 + 12 x^5 + 4 x^6)/((-1 + x)^2 (-1 + 8 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x]
%o A359621 (PARI) Vec((1 - 16*x + 97*x^2 - 210*x^3 + 84*x^4 + 12*x^5 + 4*x^6)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2) + O(x^21)) \\ _Andrew Howroyd_, Jan 26 2023
%Y A359621 Cf. A359620.
%K A359621 nonn
%O A359621 0,2
%A A359621 _Eric W. Weisstein_, Jan 07 2023
%E A359621 a(0)-a(2) prepended and terms a(8) and beyond from _Andrew Howroyd_, Jan 26 2023