A250666 Number of tilings of a 18 X n rectangle using 2n nonominoes of shape I.

1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 25, 40, 57, 76, 97, 120, 145, 172, 400, 809, 1449, 2376, 3652, 5345, 7529, 10284, 13696, 21232, 35417, 60028, 100004, 161664, 252945, 383660, 565776, 813712, 1201856, 1838369, 2895233, 4629793, 7412665, 11761912, 18384420

Offset: 0

Author

Alois P. Heinz, Nov 26 2014

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Nonomino

Crossrefs

Column k=9 of A250662.

Cf. A251078.

Programs

Maple

gf:= -(x^36 +x^32 -3*x^28 -4*x^27 -3*x^24 -3*x^23 +3*x^20 +6*x^19 +6*x^18 +3*x^16 +4*x^15 +3*x^14 -x^12 -2*x^11 -3*x^10 -4*x^9 -x^8 -x^7 -x^6 -x^5 +1) *(x-1)^8 *(x^2+x +1)^8 *(x^6+x^3+1)^8 / (x^117 +x^113 -4*x^109 -13*x^108 -4*x^105 -12*x^104 +6*x^101 +43*x^100 +78*x^99 +6*x^97 +40*x^96 +66*x^95 -4*x^93 -55*x^92 -209*x^91 -286*x^90 -4*x^89 -52*x^88 -180*x^87 -220*x^86 +x^85 +33*x^84 +225*x^83 +605*x^82 +716*x^81
+32*x^80 +200*x^79 +480*x^78 +495*x^77 -8*x^76 -120*x^75 -540*x^74 -1155*x^73 -1295*x^72 -112*x^71 -448*x^70 -840*x^69 -792*x^68 +28*x^67 +252*x^66 +840*x^65 +1518*x^64 +1744*x^63 +224*x^62 +644*x^61 +1008*x^60 +924*x^59 -56*x^58 -336*x^57 -882*x^56 -1386*x^55 -1772*x^54 -280*x^53 -616*x^52 -840*x^51 -792*x^50 +70*x^49 +294*x^48 +630*x^47 +858*x^46
+1365*x^45 +224*x^44 +392*x^43 +480*x^42 +503*x^41 -56*x^40 -168*x^39 -300*x^38 -354*x^37 -803*x^36 -112*x^35 -160*x^34 -204*x^33 -244*x^32 +28*x^31 +60*x^30 +114*x^29 +103*x^28 +362*x^27 +32*x^26 +62*x^25 +72*x^24 +90*x^23 -8*x^22 -20*x^21 -31*x^20 -13*x^19 -118*x^18 -12*x^17 -12*x^16 -12*x^15 -20*x^14 +x^13 +x^12 +x^11 -7*x^10 +22*x^9 +x^5 +x -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..60);

Formula

G.f.: See Maple program.