login
A233428
Number of tilings of a 3 X 5n rectangle with 3n pentominoes of any shape.
2
1, 56, 7670, 1082911, 153054306, 21632866165, 3057616805283, 432167457281031, 61083099363540480, 8633563135788393662, 1220278820098831948033, 172475764103555415010594, 24377944378888377125376221, 3445609736701113995818305965, 487006872816193035818432289071
OFFSET
0,2
LINKS
Wikipedia, Pentomino
FORMULA
From Vaclav Kotesovec, Mar 05 2016: (Start)
a(n) ~ c * d^n, where d = 141.34127484863151940788399760068559708960763498273966116022774034..., c = 0.3835032349236650628846889495224683008372791393401511291113817887...
a(n) = 172*a(n-1) - 4716*a(n-2) + 56595*a(n-3) - 364164*a(n-4) + 1353076*a(n-5) - 3014276*a(n-6) + 4180766*a(n-7) - 3711813*a(n-8) + 2129818*a(n-9) - 781787*a(n-10) + 178168*a(n-11) - 24000*a(n-12) + 1780*a(n-13) - 67*a(n-14) + a(n-15).
G.f.: (-1 + 116*x - 2754*x^2 + 28828*x^3 - 160178*x^4 + 509733*x^5 - 963854*x^6 + 1114401*x^7 - 801386*x^8 + 358357*x^9 - 97595*x^10 + 15483*x^11 - 1335*x^12 + 58*x^13 - x^14)/( - 1 + 172*x - 4716*x^2 + 56595*x^3 - 364164*x^4 + 1353076*x^5 - 3014276*x^6 + 4180766*x^7 - 3711813*x^8 + 2129818*x^9 - 781787*x^10 + 178168*x^11 - 24000*x^12 + 1780*x^13 - 67*x^14 + x^15).
(End)
CROSSREFS
Quintisection of column k=3 of A233427.
Sequence in context: A255960 A201240 A329104 * A183614 A082167 A006690
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 09 2013
STATUS
approved