A049853 a(n) = a(n-1) + Sum_{k=0..n-3} a(k) for n >= 2, a(0)=1, a(1)=2.

1, 2, 2, 3, 6, 11, 19, 33, 58, 102, 179, 314, 551, 967, 1697, 2978, 5226, 9171, 16094, 28243, 49563, 86977, 152634, 267854, 470051, 824882, 1447567, 2540303, 4457921, 7823106, 13728594, 24092003, 42278518, 74193627

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 2*a(n-1) - a(n-2) + a(n-3); 3 initial terms required.

a(n) = a(n-1) + a(n-2) + a(n-4) for n > 3. - Reinhard Zumkeller, Aug 06 2011

Empirical: a(n) = Sum_{k=0..floor(n/3)} A084534(n-2*k, n-3*k). - Johannes W. Meijer, Jun 17 2018

G.f.: (1 - x)*(1 + x) / (1 - 2*x + x^2 - x^3). - Colin Barker, Jun 17 2018

Maple

a := proc(n) option remember: if n<2 then n+1 else a(n-1) + add(a(k), k=0..n-3) fi end: seq(a(n), n=0..33); # Johannes W. Meijer, Jun 18 2018

Mathematica

LinearRecurrence[{2, -1, 1}, {1, 2, 2}, 40] (* Harvey P. Dale, May 12 2022 *)

Prog

(Haskell)
a049853 n = a049853_list !! n
a049853_list = 1 : 2 : 2 : 3 :
   zipWith (+) a049853_list
               (zipWith (+) (drop 2 a049853_list) (drop 3 a049853_list))
-- Reinhard Zumkeller, Aug 06 2011
(PARI) Vec((1 - x)*(1 + x) / (1 - 2*x + x^2 - x^3) + O(x^40)) \\ Colin Barker, Jun 17 2018

Crossrefs

Cf. A070550, A180662 (Ca2).

Sequence in context: A145778 A102762 A320783 * A162599 A064319 A307241

Adjacent sequences: A049850 A049851 A049852 * A049854 A049855 A049856

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved