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A250665 Number of tilings of a 16 X n rectangle using 2n octominoes of shape I. 3

%I

%S 1,1,1,1,1,1,1,1,11,23,37,53,71,91,113,137,324,665,1206,1999,3102,

%T 4579,6500,8941,14428,24963,43558,74221,122158,193995,298020,444445,

%U 682749,1087886,1781424,2948681,4861063,7903814,12610046,19701987,30702835,48251196

%N Number of tilings of a 16 X n rectangle using 2n octominoes of shape I.

%H Alois P. Heinz, <a href="/A250665/b250665.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: See Maple program.

%p gf:= -(x^12 +x^11 +x^10 +2*x^9 +2*x^8 +2*x^7 +3*x^6 +2*x^5 +x^4 +2*x^3 +x^2 +1) *(x^15 -x^12 -x^11 -x^8 -2*x^7 +2*x^5 +3*x^4 +2*x^3 -x -1) *(x-1)^7 *(x+1)^7 *(x^2+1)^7 *(x^4+1)^7 / (x^91 +x^90 +x^89 +x^88 -4*x^84 -15*x^83 -15*x^82 -15*x^81 -12*x^80 -x^79 -x^78 +5*x^77 +41*x^76

%p +96*x^75 +96*x^74 +93*x^73 +67*x^72 +12*x^71 +8*x^70 -38*x^69 -182*x^68 -347*x^67 -346*x^66 -324*x^65 -225*x^64 -59*x^63 -31*x^62 +123*x^61 +459*x^60 +789*x^59 +782*x^58 +712*x^57 +496*x^56 +159*x^55 +75*x^54 -219*x^53 -723*x^52 -1185*x^51 -1164*x^50 -1038*x^49 -744*x^48 -261*x^47 -121*x^46 +229*x^45 +733*x^44 +1195*x^43 +1160*x^42 +1020*x^41 +768*x^40

%p +271*x^39 +131*x^38 -135*x^37 -471*x^36 -808*x^35 -773*x^34 -675*x^33 -549*x^32 -177*x^31 -93*x^30 +33*x^29 +198*x^28 +384*x^27 +363*x^26 +321*x^25 +283*x^24 +76*x^23 +48*x^22 -7*x^21 -71*x^20 -147*x^19 -140*x^18 -123*x^17 -118*x^16 -35*x^15 -24*x^14 -13*x^13 -2*x^12 +16*x^11 +15*x^10 +14*x^9 +20*x^8 +x^7 +x^6 +x^5 +x^4 -1):

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

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

%Y Column k=8 of A250662.

%Y Cf. A251077.

%K nonn,easy

%O 0,9

%A _Alois P. Heinz_, Nov 26 2014

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Last modified September 19 21:11 EDT 2021. Contains 347564 sequences. (Running on oeis4.)