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%I #17 Nov 22 2020 08:20:04
%S 4,40,416,3808,33472,282752,2339072,19077632,154350592,1242703872,
%T 9977483264,79979520000,640542392320,5127428276224,41032860631040,
%U 328320884015104,2626816281149440,21015595535826944,168129300578435072,1345053647156805632,10760510547561545728
%N Number of ways to construct a triangle with longest side n using unit-length straws of two colors for the sides.
%H Lars Blomberg, <a href="/A278036/b278036.txt">Table of n, a(n) for n = 1..100</a>
%H Sergei Abramovich, <a href="https://sie.scholasticahq.com/article/4653-combinatorics-of-the-triangle-inequality-from-straws-to-experimental-mathematics-for-teachers">Combinatorics of the Triangle Inequality: From Straws to Experimental Mathematics for Teachers</a>, Spreadsheets in Education (eJSiE), Vol. 9, Issue 1, Article 1, 2016.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-104,144,640,-2304,2048).
%F G.f.: 4*x*(1 - 8*x + 28*x^2 - 24*x^3 - 32*x^4) / ((1 - 2*x) * (1 - 4*x)^2 * (1 - 8*x) * (1 - 8*x^2)). - _Colin Barker_, Nov 16 2016
%t CoefficientList[ Series[(4 (-1 + 8x - 28x^2 + 24x^3 + 32x^4))/((-1 + 4x)^2 (-1 + 10x - 8x^2 - 80x^3 + 128x^4)), {x, 0, 20}], x] (* or *)LinearRecurrence[{18, -104, 144, 640, -2304, 2048}, {4, 40, 416, 3808, 33472, 282752}, 21] (* _Robert G. Wilson v_, Nov 16 2016 *)
%o (PARI) Vec(4*x*(1-8*x+28*x^2-24*x^3-32*x^4)/((1-2*x)*(1-4*x)^2*(1-8*x)*(1-8*x^2)) + O(x^30)) \\ _Colin Barker_, Nov 16 2016
%Y Cf. A278037.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Nov 14 2016
%E More terms from _Lars Blomberg_, Nov 16 2016