A101197 - OEIS

%I #14 Jul 03 2023 07:52:11

%S 1,3,9,25,71,199,561,1577,4439,12487,35137,98857,278151,782599,

%T 2201937,6195369,17431351,49044935,137993185,388258473,1092406631,

%U 3073602311,8647907569,24331808809,68460135703,192619882695

%N Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> b}.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, -2).

%F a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3).

%F G.f.: -(x+1) / (-2*x^3+3*x^2+2*x-1).

%e a => aab => aabaabaac => aabaabaacaabaabaacaabaabb, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 25.

%p a:= n-> (<<0|1|0>, <0|0|1>, <-2|3|2>>^n. <<0, 1, 3>>)[2, 1]:

%p seq (a(n), n=0..30);  # _Alois P. Heinz_, May 06 2011

%t LinearRecurrence[{2,3,-2},{1,3,9},30] (* _Harvey P. Dale_, Jan 01 2019 *)

%Y Cf. A101399, A101400.

%Y Pairwise sums of A046672.

%K easy,nonn

%O 0,2

%A _Jeroen F.J. Laros_, Jan 22 2005

%E Terms >=1577 by _Alois P. Heinz_, May 06 2011