This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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