A233428 Number of tilings of a 3 X 5n rectangle with 3n pentominoes of any shape.

1, 56, 7670, 1082911, 153054306, 21632866165, 3057616805283, 432167457281031, 61083099363540480, 8633563135788393662, 1220278820098831948033, 172475764103555415010594, 24377944378888377125376221, 3445609736701113995818305965, 487006872816193035818432289071

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

Adjacent sequences: A233425 A233426 A233427 * A233429 A233430 A233431

Keyword

nonn

Author

Alois P. Heinz, Dec 09 2013

Status

approved