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 A271786 Expansion of 2*(1-x)*(2*x^2+4*x+1) / (1-x-x^2)^2. 3
 2, 10, 18, 38, 72, 136, 250, 454, 814, 1446, 2548, 4460, 7762, 13442, 23178, 39814, 68160, 116336, 198026, 336254, 569702, 963270, 1625708, 2739028, 4607522, 7739386, 12982530, 21750374, 36396984, 60839896, 101593498, 169482550, 282481822, 470419302 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The number of Tatami Tilings of the 3 X (2n+1) floor with one monomer at an arbitrary place (and therefore 3n+1 dimers). The sequence is an overlay of the sequence b(n) = 1, 4, 7, 14, 26,... with g.f. B(x) = x*(1+2*x^2-2*x^4-2*x^6) / (1-x^2-x^4)^2 and the sequence c(n) = 0, 2, 4, 10, 20,... with g.f. C(x) = 2*x^3/(1-x^2-x^4)^2, meaning a(n) = 2*b(n)+c(n) = 2, 10, 18, 38, 72.... The sequence b(n) counts the tatami tilings with one monomer that must be in the first of the three lanes of the 3Xn grid. The sequence c(n) counts the tatami tilings with one monomer that must be in the middle lane of the grid. By up-down symmetry b(n) counts also the tatami tilings with one monomer that must be in the last of the three lanes.  - R. J. Mathar, May 03 2016 LINKS R. J. Mathar, Re: tatami, SeqFan List of March 2016. Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1). FORMULA a(n) = 2*(A001629(n+2)+A271785(n)) . MAPLE A271786 := proc(n)     2*(A001629(n+2)+A271785(n)) ; end proc: CROSSREFS Cf. A001629, A271785, first column of A272472. Sequence in context: A173592 A018227 A092062 * A134251 A317714 A055260 Adjacent sequences:  A271783 A271784 A271785 * A271787 A271788 A271789 KEYWORD nonn,easy AUTHOR R. J. Mathar, Apr 14 2016 STATUS approved

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)