A278037 - OEIS

%I #22 Nov 22 2020 07:14:50

%S 10,300,9405,271701,7586055,207778365,5643858222,152750888154,

%T 4128157816596,111500380788894,3010918493945871,81298895147719695,

%U 2195110845820568241,59268393196729777359,1600250528431547974368,43206802254989454564468,1166584027787796828029022

%N Number of ways to construct a triangle with longest side n using unit-length straws of three colors for the sides.

%H Lars Blomberg, <a href="/A278037/b278037.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 (48,-675,2592,12393,-104976,177147).

%F G.f.: x*(10 - 180*x + 1755*x^2 - 3159*x^3 - 8748*x^4) / ((1 - 3*x) * (1 - 9*x)^2 * (1 - 27*x) * (1 - 27*x^2)). - _Colin Barker_, Nov 16 2016

%t LinearRecurrence[{48,-675,2592,12393,-104976,177147},{10,300,9405,271701,7586055,207778365},20] (* _Harvey P. Dale_, May 08 2018 *)

%o (PARI) Vec(x*(10-180*x+1755*x^2-3159*x^3-8748*x^4)/((1-3*x)*(1-9*x)^2*(1-27*x)*(1-27*x^2)) + O(x^30)) \\ _Colin Barker_, Nov 16 2016

%Y Cf. A278036.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Nov 14 2016

%E More terms from _Lars Blomberg_, Nov 16 2016