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A084478 Number of tilings of a 5 X 3n rectangle with right trominoes. 5
72, 384, 8544, 76800, 1168512, 12785664, 170678784, 2014648320, 25633231872, 311423852544, 3892030055424, 47803588208640, 593425578949632, 7318730222874624, 90624271197041664, 1119402280975349760, 13847850677651745792, 171150049715628539904 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

A tromino is a 3-celled L-shaped piece (a 2 X 2 square with one of the four cells omitted). - N. J. A. Sloane, Mar 28 2017

There is a sign typo with respect to the g.f. in the paper.

LINKS

Colin Barker, Table of n, a(n) for n = 2..900

C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999.

Index entries for linear recurrences with constant coefficients, signature (2,103,280,380).

FORMULA

G.f.: -1 + (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4) / (1 - 2*z - 103*z^2 - 280*z^3 - 380*z^4).

a(n) = 2*a(n-1) + 103*a(n-2) + 280*a(n-3) + 380*a(n-4) for n > 4. - Colin Barker, Mar 27 2017

MATHEMATICA

LinearRecurrence[{2, 103, 280, 380}, {72, 384, 8544, 76800}, 20] (* Jean-Fran├žois Alcover, Jan 07 2019 *)

PROG

(PARI) Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 103*x^2 - 280*x^3 - 380*x^4) + O(x^30)) \\ Colin Barker, Mar 27 2017

CROSSREFS

Cf. A084477, A084479, A084480, A084481.

Sequence in context: A192792 A303621 A084479 * A187158 A164377 A156632

Adjacent sequences:  A084475 A084476 A084477 * A084479 A084480 A084481

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, May 27 2003

STATUS

approved

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Last modified September 21 22:17 EDT 2019. Contains 327284 sequences. (Running on oeis4.)