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A250665 Number of tilings of a 16 X n rectangle using 2n octominoes of shape I. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 02:42 EDT 2021. Contains 346282 sequences. (Running on oeis4.)