OFFSET
0,1
COMMENTS
From Wajdi Maaloul, Jun 23 2022: (Start)
For n>0, a(n) is the number of ways to tile the figure below with squares and dominoes (a strip of length n+2 that contains two vertical strip of height 3 in its first and third tiles).
_ _
|_| |_|
|_|_|_|_____ _
|_|_|_|_|_|_|...|_|
(End)
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1, 1).
FORMULA
From G. C. Greubel, Jul 10 2017: (Start)
a(n+2) = a(n+1) + a(n) with a(0) = 10, a(1) = 21.
a(n) = 11*Fibonacci(n) + 10*Fibonacci(n+1).
a(n) = 9*Fibonacci(n+2) + Lucas(n+1).
G.f.: (10 + 11*x)/(1 - x - x^2).
E.g.f.: (1/sqrt(5))*exp(x/2)*(32*sinh(sqrt(5)*x/2) + 10*sqrt(5)*cosh(sqrt(5)*x/2)). (End)
MATHEMATICA
Join[{a=10, b=21}, Table[c=a+b; a=b; b=c, {n, 60}]]
CoefficientList[Series[(10 + 11*x)/(1 - x - x^2), {x, 0, 50}], x] (* G. C. Greubel, Jul 10 2017 *)
LinearRecurrence[{1, 1}, {10, 21}, 40] (* Harvey P. Dale, Aug 01 2024 *)
PROG
(PARI) x='x+O('x^50); Vec((10 + 11*x)/(1 - x - x^2)) \\ G. C. Greubel, Jul 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Feb 28 2011
STATUS
approved