A226550 Number of squares in all tilings of a 7 X n rectangle using integer-sided square tiles.

0, 7, 180, 1625, 16936, 157279, 1426734, 12582472, 108971358, 929801662, 7842704798, 65526395993, 543197940936, 4473218574611, 36628689696182, 298465716569236, 2421637058537566, 19574314969125483, 157692516088571216, 1266593481935599039, 10146033357194978996

Offset

0,2

Links

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

Formula

G.f.: (36*x^42 +492*x^41 +97*x^40 -1280*x^39 +1374*x^38 +3986*x^37 -3294*x^36 -12844*x^35 -17178*x^34 -5612*x^33 -8231*x^32 -68874*x^31 -38198*x^30 +87106*x^29 +79120*x^28 +342382*x^27 +1028045*x^26 +1129834*x^25 +797531*x^24 +933000*x^23 +781401*x^22 -15364*x^21 -688028*x^20 -1167490*x^19 -1199056*x^18 -495108*x^17 +175219*x^16 +637592*x^15 +810642*x^14 +590608*x^13 +255600*x^12 -62792*x^11 -226422*x^10 -130944*x^9 -26229*x^8 +21996*x^7 +25573*x^6 +5782*x^5 -3711*x^4 -1682*x^3 +174*x^2 +138*x+7)*x / (6*x^25 +11*x^24 -9*x^23 -10*x^22 +39*x^21 +12*x^20 -70*x^19 -281*x^18 -403*x^17 -110*x^16 -118*x^15 -790*x^14 -179*x^13 +466*x^12 +327*x^11 +669*x^10 +1028*x^9 +231*x^8 -45*x^7 -284*x^6 -273*x^5 -61*x^4 +45*x^3 +31*x^2 +3*x-1)^2.

Crossrefs

Column k=7 of A226545.

Cf. A219926.

Sequence in context: A221110 A142256 A226427 * A141983 A080484 A212944

Adjacent sequences: A226547 A226548 A226549 * A226551 A226552 A226553

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 10 2013

Status

approved