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A272471 Triangle T(n,m) by rows: The number of tatami tilings of a 2 X n grid with dimers and 2*m monomers. 4
1, 1, 2, 4, 3, 9, 1, 4, 18, 7, 6, 35, 26, 1, 9, 64, 73, 10, 13, 112, 179, 52, 1, 19, 192, 403, 194, 13, 28, 323, 850, 597, 87, 1, 41, 534, 1707, 1624, 408, 16, 60, 872, 3303, 4046, 1532, 131, 1, 88, 1410, 6203, 9428, 4951, 742, 19, 129, 2260, 11366, 20847, 14361, 3308 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

A. Erickson, F. Ruskey, J. Woodcock, M. Schurch, Auspicious tatami mat arrangements, arXiv:1103.3309 (2011).

FORMULA

G.f. x*(y^2 +2*x*y^2 +x^2*y^2 +1 -x^3)/(x^4 -x^3*y^2 -x^3 -x^2*y^2 +x^2 -2*x +1). - R. J. Mathar, May 01 2016

EXAMPLE

The triangle starts in row n=1 as:

1,1;

2,4;

3,9,1;

4,18,7;

6,35,26,1;

9,64,73,10;

13,112,179,52,1;

19,192,403,194,13;

28,323,850,597,87,1;

41,534,1707,1624,408,16;

60,872,3303,4046,1532,131,1;

88,1410,6203,9428,4951,742,19;

129,2260,11366,20847,14361,3308,184;

189,3596,20407,44194,38369,12472,1223,22;

277,5687,36018,90492,96071,41559,6330,246,1;

406,8946,62648,179982,228224,125942,27382,1878,25;

595,14007,107602,349244,519071,353929,103504,11084,317,1;

872,21842,182800,663470,1138094,935298,352234,54226,2734,28;

1278,33937,307581,1237436,2418496,2348345,1101887,229886,18137,397,1;

1873,52560,513165,2271066,5002459,5646544,3216889,870490,99142,3818,31;

2745,81168,849726,4109303,10106351,13082702,8864264,3008357,466676,28137,486,1;

4023,125022,1397565,7342252,19999147,29352862,23256181,9640660,1949989,170104,5157,34;

5896,192117,2284716,12971722,38856275,64030031,58492346,28994720,7393154,881310,41813,584,1;

8641,294588,3714618,22686720,74268850,136248856,141811450,82607092,25852870,4033500,277165,6778,37;

MATHEMATICA

Select[Flatten[CoefficientList[CoefficientList[Series[x*(y^2 + 2*x*y^2 + x^2*y^2 + 1 - x^3)/(x^4 - x^3*y^2 - x^3 - x^2*y^2 + x^2 - 2*x + 1), {x, 0, 10}, {y, 0, 10}], x], y]], # != 0 &] (* G. C. Greubel, Apr 28 2017 *)

CROSSREFS

Cf. A180965 (row sums), A000930 (column m=0), A046741 (without tatami condition).

Sequence in context: A243051 A253791 A021045 * A155749 A198931 A293779

Adjacent sequences:  A272468 A272469 A272470 * A272472 A272473 A272474

KEYWORD

nonn,tabf

AUTHOR

R. J. Mathar, Apr 30 2016

STATUS

approved

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Last modified July 21 22:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)