A278036 Number of ways to construct a triangle with longest side n using unit-length straws of two colors for the sides.

4, 40, 416, 3808, 33472, 282752, 2339072, 19077632, 154350592, 1242703872, 9977483264, 79979520000, 640542392320, 5127428276224, 41032860631040, 328320884015104, 2626816281149440, 21015595535826944, 168129300578435072, 1345053647156805632, 10760510547561545728

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 (18,-104,144,640,-2304,2048).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A278037.

Sequence in context: A299867 A093141 A220965 * A221588 A114468 A264112

Adjacent sequences: A278033 A278034 A278035 * A278037 A278038 A278039

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 14 2016

Extensions

More terms from Lars Blomberg, Nov 16 2016

Status

approved