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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

(list; graph; refs; listen; history; text; internal format)

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

URL: https://oeis.org/A278036

⇱ A278036 - OEIS