A272472 Triangle T(n,m) by rows: The number of tatami tilings of a 3 by n grid with dimers and m monomers.

0, 2, 0, 1, 3, 0, 9, 0, 1, 0, 10, 0, 12, 4, 0, 27, 0, 13, 0, 18, 0, 56, 0, 16, 6, 0, 75, 0, 97, 0, 18, 0, 38, 0, 198, 0, 152, 0, 18, 10, 0, 177, 0, 433, 0, 214, 0, 18, 0, 72, 0, 570, 0, 836, 0, 282, 0, 18, 16, 0, 393, 0, 1517, 0, 1442, 0, 354, 0, 18, 0, 136

Offset

1,2

Links

Table of n, a(n) for n=1..71.

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

Formula

G.f. x *(x^4*y^3 +7*x*y^2 +3*x +2*y +y^3 +x^6*y +3*x^2*y -x^3*y^2 -6*x^4*y -x^2*y^5 +x^2*y^3 +y^3*x^6 -2*y^4*x^5 -2*x^3 -2*x^5 +y^5*x^4 -x^3*y^4 -x^5*y^2 +x^7) / (x^6 +x^5*y -2*x^4*y^2 -2*x^2 -x*y +1). - R. J. Mathar, May 01 2016

Example

The triangle starts in row n=1 and column m=0 as:
0,2,0,1;
3,0,9,0,1;
0,10,0,12;
4,0,27,0,13;
0,18,0,56,0,16;
6,0,75,0,97,0,18;
0,38,0,198,0,152,0,18;
10,0,177,0,433,0,214,0,18;
0,72,0,570,0,836,0,282,0,18;
16,0,393,0,1517,0,1442,0,354,0,18;
0,136,0,1478,0,3472,0,2292,0,426,0,18;
26,0,829,0,4571,0,7052,0,3410,0,498,0,18;
0,250,0,3554,0,12070,0,13076,0,4808,0,570,0,18;
42,0,1691,0,12479,0,28158,0,22480,0,6494,0,642,0,18;
0,454,0,8108,0,37222,0,59530,0,36308,0,8468,0,714,0,18;
68,0,3359,0,31729,0,97766,0,115948,0,55672,0,10730,0,786,0,18;
0,814,0,17768,0,105238,0,231622,0,210880,0,81708,0,13280,0,858,0,18;
110,0,6537,0,76483,0,306606,0,503348,0,361878,0,115568,0,16118,0,930,0,18;
0,1446,0,37736,0,278626,0,803060,0,1016880,0,590846,0,158404,0,19244,0,1002,0,18;
178,0,12511,0,176833,0,889916,0,1923278,0,1929730,0,924216,0,211368,0,22658,0,1074,0,18;
0,2548,0,78144,0,700670,0,2549216,0,4268026,0,3469042,0,1392996,0,275612,0,26360,0,1146,0,18;
288,0,23617,0,395387,0,2430464,0,6661414,0,8867630,0,5948792,0,2032802,0,352288,0,30350,0,1218,0,18;
0,4460,0,158492,0,1690478,0,7547920,0,16089358,0,17395888,0,9787628,0,2883858,0,442548,0,34628,0,1290,0,18;
466,0,44067,0,860069,0,6319840,0,21344172,0,36292416,0,32446518,0,15527142,0,3990996,0,547544,0,39194,0,1362,0,18;

Crossrefs

Cf. A180970 (row sums), A068922 (column m=0), A271786 (column m=1), A272471 (2 by n grid), A100245 (row reversed without tatami condition).

Sequence in context: A331533 A089994 A178107 * A355536 A100260 A165317

Adjacent sequences: A272469 A272470 A272471 * A272473 A272474 A272475

Keyword

tabf,nonn

Author

R. J. Mathar, Apr 30 2016

Status

approved