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URL: https://oeis.org/A278037

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A278037
Number of ways to construct a triangle with longest side n using unit-length straws of three colors for the sides.
2
10, 300, 9405, 271701, 7586055, 207778365, 5643858222, 152750888154, 4128157816596, 111500380788894, 3010918493945871, 81298895147719695, 2195110845820568241, 59268393196729777359, 1600250528431547974368, 43206802254989454564468, 1166584027787796828029022
OFFSET
1,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 14 2016
EXTENSIONS
More terms from Lars Blomberg, Nov 16 2016
STATUS
approved