A219927 Number of tilings of an 8 X n rectangle using integer-sided square tiles.

1, 1, 34, 277, 3049, 31497, 329350, 3435392, 35863972, 374285478, 3906605183, 40773605243, 425562898029, 4441677458152, 46358636450427, 483853831650209, 5050074056261222, 52708577944998395, 550129399697072615, 5741804607960538038, 59928300863912394900

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

G.f.: see Maple program.

Maple

gf:= -(60*x^40 +136*x^39 -321*x^38 -1038*x^37 -2045*x^36 +2501*x^35 +4393*x^34 +7347*x^33 +4372*x^32 -4825*x^31 -13838*x^30 -19585*x^29 -9331*x^28 -40213*x^27 +19891*x^26 +57417*x^25 +68058*x^24 +10427*x^23 -8789*x^22 +6040*x^21 -76684*x^20 -81024*x^19 -16484*x^18 +11908*x^17 +42083*x^16 +63711*x^15 +19938*x^14 -2290*x^13 -18240*x^12 -18560*x^11 -7633*x^10 +291*x^9 +4194*x^8 +2502*x^7 +378*x^6 -361*x^5 -240*x^4 -33*x^3 +27*x^2 +5*x -1) /
(60*x^48 +256*x^47 +35*x^46 -1488*x^45 -4435*x^44 -2543*x^43 +7032*x^42 +16610*x^41 +23043*x^40 +18924*x^39 +3186*x^38 -57091*x^37 -115830*x^36 -141242*x^35 +18849*x^34 +39846*x^33 +240064*x^32 +433164*x^31 +162501*x^30 -692061*x^29 -641988*x^28 +446013*x^27 +530385*x^26 +657974*x^25 -654746*x^24 -708014*x^23 -43614*x^22 -370550*x^21 +356235*x^20 +824516*x^19 +224413*x^18 -94736*x^17 -143852*x^16 -344353*x^15 -110166*x^14 +15107*x^13 +55317*x^12 +51581*x^11 +29259*x^10 +6818*x^9 -5977*x^8 -8807*x^7 -2453*x^6 +1175*x^5 +708*x^4 +15*x^3 -55*x^2 -6*x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Crossrefs

Column k=8 of A219924.

Cf. A226551.

Sequence in context: A241698 A159776 A295917 * A228284 A248076 A301543

Adjacent sequences: A219924 A219925 A219926 * A219928 A219929 A219930

Keyword

nonn

Author

Alois P. Heinz, Dec 01 2012

Status

approved