OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..5560
Michael A. Allen, Combinations without specified separations and restricted-overlap tiling with combs, arXiv:2210.08167 [math.CO], 2022.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1).
FORMULA
G.f.: (1+z+z^3)/(1-z-z^2+z^3-z^4).
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4); a(0)=1, a(1)=2, a(2)=3, a(3)=5.
a(n) = A130136(n,0).
EXAMPLE
a(4)=7 because from the 8 Fibonacci binary words of length 4 only 0110 does not qualify.
MAPLE
a[0]:=1: a[1]:=2: a[2]:=3: a[3]:=5: for n from 4 to 45 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-4] od: seq(a[n], n=0..45);
MATHEMATICA
LinearRecurrence[{1, 1, -1, 1}, {1, 2, 3, 5}, 40] (* Jean-François Alcover, Aug 25 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 13 2007
STATUS
approved