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A232621
The number of vertically fault-free 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
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).
FORMULA
G.f.: (1 + x - 18*x^2 + 13*x^3 - x^4)/((1-x)*(1 - 6*x + x^2)).
a(n) = 1 + 6*A001653(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
Sequence in context: A121097 A121093 A296830 * A303176 A209484 A209343
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 27 2013
STATUS
approved