A272471 - OEIS

%I #19 Apr 28 2017 22:40:26

%S 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,

%T 194,13,28,323,850,597,87,1,41,534,1707,1624,408,16,60,872,3303,4046,

%U 1532,131,1,88,1410,6203,9428,4951,742,19,129,2260,11366,20847,14361,3308

%N Triangle T(n,m) by rows: The number of tatami tilings of a 2 X n grid with dimers and 2*m monomers.

%H G. C. Greubel, <a href="/A272471/b272471.txt">Table of n, a(n) for the first 100 rows, flattened</a>

%H A. Erickson, F. Ruskey, J. Woodcock, M. Schurch, <a href="http://arxiv.org/abs/1103.3309">Auspicious tatami mat arrangements</a>, arXiv:1103.3309 (2011).

%F 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

%e The triangle starts in row n=1 as:

%e 1,1;

%e 2,4;

%e 3,9,1;

%e 4,18,7;

%e 6,35,26,1;

%e 9,64,73,10;

%e 13,112,179,52,1;

%e 19,192,403,194,13;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%t 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 *)

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

%K nonn,tabf

%O 1,3

%A _R. J. Mathar_, Apr 30 2016