OFFSET
0,2
COMMENTS
Lengths of successive words (starting with a) under the substitution: {a -> ab, b -> aac, c -> d, d -> b}.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,1,-1).
FORMULA
G.f.: (1+x+x^2)/(1-x-2*x^2-x^3+x^4). - G. C. Greubel, Apr 03 2018
EXAMPLE
a(0) = 1, a(1) = 2, a(2) = 5, a(3) = 10, a(4) = 21, a(5) = 44
MATHEMATICA
a[0] = 1; a[1] = 2; a[2] = 5; a[3] = 10; a[n_] := a[n] = a[n - 1] + 2a[n - 2] + a[n - 3] - a[n - 4]; Table[ a[n], {n, 0, 30}] (* Robert G. Wilson v, Jan 15 2005 *)
LinearRecurrence[{1, 2, 1, -1}, {1, 2, 5, 10}, 40] (* Harvey P. Dale, Oct 24 2017 *)
PROG
(PARI) x='x+O('x^30); Vec((1+x+x^2)/(1-x-2*x^2-x^3+x^4)) \\ G. C. Greubel, Apr 03 2018
(Magma) I:=[1, 2, 5, 10]; [n le 4 select I[n] else Self(n-1) + 2*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x+x^2)/(1-x-2*x^2-x^3+x^4))); // G. C. Greubel, Apr 03 2018
(GAP) a:=[1, 2, 5, 10];; for n in [5..35] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Apr 03 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeroen F.J. Laros, Jan 15 2005
EXTENSIONS
More terms from Robert G. Wilson v, Jan 15 2005
STATUS
approved