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

1, 1, 1, 1, 1, 1, 1, 1, 11, 23, 37, 53, 71, 91, 113, 137, 324, 665, 1206, 1999, 3102, 4579, 6500, 8941, 14428, 24963, 43558, 74221, 122158, 193995, 298020, 444445, 682749, 1087886, 1781424, 2948681, 4861063, 7903814, 12610046, 19701987, 30702835, 48251196

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, Octomino

Crossrefs

Column k=8 of A250662.

Cf. A251077.

Programs

Maple

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
+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
+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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..60);

Formula

G.f.: See Maple program.