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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 (list; graph; refs; listen; history; text; internal format)
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^3-x^4+x+1)/((1-x)*(1-6*x+x^2)).

a(n) = 1 + 3*A075870(n) for n>1. [Bruno Berselli, Nov 27 2013]

a(n) = 6*a(n-1)-a(n-2)-4, n>=4. - R. J. Mathar, Nov 07 2015

a(n) = 1+3/2*(3-2*sqrt(2))^n*(2+sqrt(2))+(3-3/sqrt(2))*(3+2*sqrt(2))^n for n>1. - Colin Barker, Mar 05 2016

PROG

(PARI) Vec((-18*x^2+13*x^3-x^4+x+1)/((1-x)*(1-6*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

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)