A250666 - OEIS

%I #12 Feb 06 2017 18:28:04

%S 1,1,1,1,1,1,1,1,1,12,25,40,57,76,97,120,145,172,400,809,1449,2376,

%T 3652,5345,7529,10284,13696,21232,35417,60028,100004,161664,252945,

%U 383660,565776,813712,1201856,1838369,2895233,4629793,7412665,11761912,18384420

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

%H Alois P. Heinz, <a href="/A250666/b250666.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Nonomino">Nonomino</a>

%F G.f.: See Maple program.

%p 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

%p +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

%p +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):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..60);

%Y Column k=9 of A250662.

%Y Cf. A251078.

%K nonn,easy

%O 0,10

%A _Alois P. Heinz_, Nov 26 2014