A233428 - OEIS

%I #13 Feb 07 2017 16:58:03

%S 1,56,7670,1082911,153054306,21632866165,3057616805283,

%T 432167457281031,61083099363540480,8633563135788393662,

%U 1220278820098831948033,172475764103555415010594,24377944378888377125376221,3445609736701113995818305965,487006872816193035818432289071

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

%H Alois P. Heinz, <a href="/A233428/b233428.txt">Table of n, a(n) for n = 0..200</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>

%F From _Vaclav Kotesovec_, Mar 05 2016: (Start)

%F a(n) ~ c * d^n, where d = 141.34127484863151940788399760068559708960763498273966116022774034..., c = 0.3835032349236650628846889495224683008372791393401511291113817887...

%F 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).

%F 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).

%F (End)

%Y Quintisection of column k=3 of A233427.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 09 2013