

A232621


The number of indecomposable domino tilings of the 5 X (2n) board.


1



1, 8, 31, 175, 1015, 5911, 34447, 200767, 1170151, 6820135, 39750655, 231683791, 1350352087, 7870428727, 45872220271, 267362892895, 1558305137095, 9082467929671, 52936502440927, 308536546715887, 1798282777854391, 10481160120410455, 61088677944608335
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OFFSET

0,2


COMMENTS

A003775 counts the tilings of the 5 X (2n) board, and this sequence here counts only those that cannot be broken into tilings of two or more smaller 5 X (2n') boards with edge lengths n' < n by cutting "vertically" through the tiling parallel to the "short" side of length 5.
Technically speaking this is the inverse INVERT transform of A003775 (see the comment in A005178).


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,7,1).


FORMULA

G.f.: (18*x^2+13*x^3x^4+x+1)/((1x)*(16*x+x^2)).
a(n) = 1 + 3*A075870(n) for n>1. [Bruno Berselli, Nov 27 2013]
a(n) = 6*a(n1)a(n2)4, n>=4.  R. J. Mathar, Nov 07 2015
a(n) = 1+3/2*(32*sqrt(2))^n*(2+sqrt(2))+(33/sqrt(2))*(3+2*sqrt(2))^n for n>1.  Colin Barker, Mar 05 2016


PROG

(PARI) Vec((18*x^2+13*x^3x^4+x+1)/((1x)*(16*x+x^2)) + O(x^30)) \\ Colin Barker, Mar 05 2016


CROSSREFS

Cf. A003775, A068924.
Sequence in context: A121097 A121093 A296830 * A303176 A209484 A209343
Adjacent sequences: A232618 A232619 A232620 * A232622 A232623 A232624


KEYWORD

nonn,easy


AUTHOR

R. J. Mathar, Nov 27 2013


STATUS

approved



