A104204 If n==0 (mod 3) then a(n)=a(n-1); if n==1 (mod 3) then a(n)=a(n-2)+a(n-3); if n==2 (mod 3) then a(n)=a(n-3)+a(n-4)+a(n-5).

1, 1, 2, 3, 5, 4, 4, 9, 12, 12, 21, 25, 25, 46, 58, 58, 104, 129, 129, 233, 291, 291, 524, 653, 653, 1177, 1468, 1468, 2645, 3298, 3298, 5943, 7411, 7411, 13354, 16652, 16652, 30006, 37417, 37417, 67423, 84075, 84075, 151498, 188915, 188915, 340413, 424488

Offset

0,3

Comments

A sequentially switched sequence modulo 3.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1,0,0,-1).

Formula

From Colin Barker, Nov 18 2015: (Start)

a(n) = 2*a(n-3)+a(n-6)-a(n-9) for n>11.

G.f.: -(x^11+x^10-2*x^9-2*x^8+2*x^7+3*x^6-3*x^4-x^3-2*x^2-x-1) / (x^9-x^6-2*x^3+1).

(End)

Maple

a:= proc(n) option remember; add(a(n-i), i=1+(n mod 3)..1+2*(n mod 3)) end proc:
a(0):= 1: a(1):= 1: a(2):= 2: a(3):= 3: a(4):= 5:
seq(a(n), n=0..100); # Robert Israel, Nov 18 2015

Mathematica

a[n_Integer?Positive] := If[Mod[n, 3] == 0, a[n] = a[n - 1], If[Mod[n, 3] == 1, a[n] = a[n - 2] + a[n - 3], a[n] = a[n - 3] + a[n - 4] + a[n - 5]]] a[0] = 1; a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 5; aa = Table[a[n], {n, 0, 200}]

Prog

(PARI) Vec(-(x^11+x^10-2*x^9-2*x^8+2*x^7+3*x^6-3*x^4-x^3-2*x^2-x-1)/(x^9-x^6-2*x^3+1) + O(x^60)) \\ Colin Barker, Nov 18 2015

Crossrefs

Sequence in context: A023818 A102149 A321782 * A131296 A371216 A267808

Adjacent sequences: A104201 A104202 A104203 * A104205 A104206 A104207

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 13 2005

Extensions

Typos in title and formula fixed by Colin Barker, Nov 18 2015

Status

approved