A101400 a(n) = a(n-1) + 2*a(n-2) + a(n-3) - a(n-4).

1, 2, 5, 10, 21, 44, 91, 190, 395, 822, 1711, 3560, 7409, 15418, 32085, 66770, 138949, 289156, 601739, 1252230, 2605915, 5422958, 11285279, 23484880, 48872481, 101704562, 211649125, 440445850, 916576181, 1907412444, 3969361531

Offset: 0

Author

Jeroen F.J. Laros, Jan 15 2005

Keywords

• nonn
• easy

Comments

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

Examples

			a(0) = 1, a(1) = 2, a(2) = 5, a(3) = 10, a(4) = 21, a(5) = 44
		

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).

Crossrefs

Cf. A092886, A105309.

Programs

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

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]]; // G. C. Greubel, Apr 03 2018

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x+x^2)/(1-x-2*x^2-x^3+x^4))); // G. C. Greubel, Apr 03 2018

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 *)

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

Formula

G.f.: (1+x+x^2)/(1-x-2*x^2-x^3+x^4). - G. C. Greubel, Apr 03 2018

Extensions

More terms from Robert G. Wilson v, Jan 15 2005