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%I #9 May 02 2016 05:05:17
%S 1,3,1,4,18,7,4,27,13,2,32,32,3,52,64,7,3,62,133,40,3,99,269,110,9,5,
%T 152,437,280,48,5,163,730,669,138,9,6,258,1243,1318,433,48,8,343,1823,
%U 2670,1239,154,9,8,408,2949,5240,2849,600,48,11,632,4577
%N Triangle T(n,m) by rows: the number of tatami tilings of a 4 by n grid with 2*m monomers.
%C The number of squares in the 4 by n floor is even, so the number of tilings with an odd number of monomers is zero.
%F G.f. x*( -1 -8*x^7*y^2 +21*x^5*y^2 -7*x^7*y^6 +4*x^3*y^2 -3*x^7 +2*x^5 -8*x^2*y^2 -4*x^8*y^4 -3*x -6*x*y^4 -15*x*y^2 -2*x^3*y^4 -6*x^8 -5*x^10*y^2 -5*x^9*y^2 -y^4 -2*x^8*y^2 -3*y^2 -8*x^11*y^2 +5*x^11*y^4 -3*x^2*y^4 -2*x^5*y^6 +2*x^13 +x^12 +x^11 +x^6 -7*x^7*y^4 +x^7*y^8 +11*x^4*y^2 -3*x^9 -15*x^10*y^4 -2*x^10*y^6 +18*x^9*y^4 +36*x^6*y^4 +20*x^6*y^2 -17*x^ 5*y^4 -8*x^4*y^4 +4*x^3 +8*x^6*y^6 +5*x^4 +2*x^9*y^6 -y^8*x^6 +6*y^6*x^3 +y^6*x^2)/ (x^11 -x^10 +2*x^9 -3*x^9*y^2 +x^8*y^2 -2*x^8 +x^7 +x^6*y^4 -5*x^6*y^2 -3*x^6 +2*x^5 +5*x^5*y^2 +x^4*y^2 -2*x^4 -x^3*y^2 +2*x^3 +x^2*y^2 +x -1). - _R. J. Mathar_, May 01 2016
%e The triangle starts in row n=1 and column m=0 as:
%e 1,3,1;
%e 4,18,7;
%e 4,27,13;
%e 2,32,32;
%e 3,52,64,7;
%e 3,62,133,40;
%e 3,99,269,110,9;
%e 5,152,437,280,48;
%e 5,163,730,669,138,9;
%e 6,258,1243,1318,433,48;
%e 8,343,1823,2670,1239,154,9;
%e 8,408,2949,5240,2849,600,48;
%e 11,632,4577,9011,6655,1927,172,9;
%e 13,746,6287,16184,14697,4930,777,48;
%e 14,971,9928,28135,28805,13089,2669,190,9;
%e 19,1394,14234,44806,58022,32176,7501,954,48;
%e 21,1610,19501,75702,111795,70427,22344,3445,208,9;
%e 25,2224,29785,121302,199354,157078,59859,10576,1131,48;
%e 32,2909,40073,184597,366553,331449,143611,34646,4257,226,9;
%e 35,3464,55939,298278,644436,651772,350855,99300,14167,1308,48;
%e 44,4820,81474,449995,1081033,1303651,802565,258303,50095,5105,244,9;
%e 53,5924,106460,670726,1868914,2488996,1719501,684338,151835,18274,1485,48;
%e 60,7408,150672,1040424,3077401,4548409,3716945,1678785,425017,68761,5989,262,9;
%e 76,9972,208211,1503372,4956628,8434302,7641320,3879356,1208052,218806,22897,1662,48;
%Y Cf. A192090 (row sums), A068923 (column m=0), A272472 (3 by n grid), A100265 (without tatami condition, reversed rows).
%K nonn,tabf
%O 1,2
%A _R. J. Mathar_, Apr 30 2016
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