OFFSET
1,2
LINKS
Andrew Woods, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (2,15,-1,-26,5,6).
FORMULA
Recurrence: a(n) = 2*a(n-1)+15*a(n-2)-a(n-3)-26*a(n-4)+5*a(n-5)+6*a(n-6) for n>6, a(1)=1, a(2)=12, a(3)=39, a(4)=233, a(5)=1018, a(6)=5191.
G.f.: x*(1+10*x-24*x^3+5*x^4+6*x^5)/((1-x)*(1-x-16*x^2-15*x^3+11*x^4+6*x^5)). [Bruno Berselli, Jun 04 2013]
EXAMPLE
For n=2 the a(2)=12 solutions are:
'_ _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ _
|_|_|_| |_|_| | |_| |_| |_| | | |_| | | |_|_|
|_|_|_| |_|_|_| |_|_|_| |_|_|_| |_|___| |_|_|_|
'_ _ _ _ _ _ ___ _ _ _ _ _ ___ ___ _
| |_| | | | |_| | |_| | | | | | | | | | |
|_|_|_| |_|_|_| |___|_| |_|_|_| |_|___| |___|_|
'
Note that the 1 x 2 tiles must point in the direction of increasing n.
MATHEMATICA
CoefficientList[Series[(1 + 10 x - 24 x^3 + 5 x^4 + 6 x^5)/((1 - x) (1 - x - 16 x^2 - 15 x^3 + 11 x^4 + 6 x^5)), {x, 0, 20}], x] (* Bruno Berselli, Jun 04 2013 *)
LinearRecurrence[{2, 15, -1, -26, 5, 6}, {1, 12, 39, 233, 1018, 5191}, 21] (* T. D. Noe, Jun 04 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew Woods, Jun 04 2013
STATUS
approved