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

0,9

Links

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

Wikipedia, Octomino

Formula

G.f.: See Maple program.

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);

Crossrefs

Column k=8 of A250662.

Cf. A251077.

Sequence in context: A280915 A139493 A275591 * A339080 A077345 A130282

Adjacent sequences: A250662 A250663 A250664 * A250666 A250667 A250668

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 26 2014

Status

approved