OFFSET
0,3
COMMENTS
Without the restriction one gets the Fibonacci numbers, A000045.
Might be called the no-tri-bonacci numbers.
LINKS
Brian Rice, Proof of the recurrence
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1).
FORMULA
a(n) = a(n-1) + a(n-4) for n>4; g.f.: (1+x^2+x^4)/(1-x-x^4). Also a(n) = a(n-2) + a(n-4) + a(n-5).
EXAMPLE
For example (using 1's to denote squares and 2's to denote dominoes), a(6)=7 because you have the tilings 11211, 1122, 1212, 1221, 2112, 2121 and 2211 and no others.
MATHEMATICA
Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {1, 2, 2, 4}, 50]] (* Harvey P. Dale, Jul 26 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Barry Cipra, Mar 03 2008
STATUS
approved