A278037 Number of ways to construct a triangle with longest side n using unit-length straws of three colors for the sides.

10, 300, 9405, 271701, 7586055, 207778365, 5643858222, 152750888154, 4128157816596, 111500380788894, 3010918493945871, 81298895147719695, 2195110845820568241, 59268393196729777359, 1600250528431547974368, 43206802254989454564468, 1166584027787796828029022

Offset

1,1

Links

Lars Blomberg, Table of n, a(n) for n = 1..100

Sergei Abramovich, Combinatorics of the Triangle Inequality: From Straws to Experimental Mathematics for Teachers, Spreadsheets in Education (eJSiE), Vol. 9, Issue 1, Article 1, 2016.

Index entries for linear recurrences with constant coefficients, signature (48,-675,2592,12393,-104976,177147).

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A278036.

Sequence in context: A069672 A129005 A162729 * A275652 A221953 A293963

Adjacent sequences: A278034 A278035 A278036 * A278038 A278039 A278040

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 14 2016

Extensions

More terms from Lars Blomberg, Nov 16 2016

Status

approved