A343885 a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4), with a(1) = a(2) = a(3) = a(4) = 1.

1, 1, 1, 1, 2, 3, 3, 3, 5, 8, 9, 9, 13, 21, 26, 27, 35, 55, 73, 80, 97, 145, 201, 233, 274, 387, 547, 667, 781, 1048, 1481, 1881, 2229, 2877, 4010, 5243, 6339, 7983, 10897, 14496, 17921, 22305, 29777, 39889, 50338, 62531, 81859, 109555, 140565, 175400, 226249, 300969

Offset

1,5

Comments

Lim_{n->infinity} a(n)/a(n-1) = 1.29064880134670962239...

Links

Table of n, a(n) for n=1..52.

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

Formula

G.f.: x*(1 + x^2)/(1 - x + x^2 - x^3 - x^4). - Andrew Howroyd, May 02 2021

Prog

(PARI) Vec((1 + x^2)/(1 - x + x^2 - x^3 - x^4) + O(x^50)) \\ Andrew Howroyd, May 02 2021
(PARI) my(p=Mod('x, 'x^4-'x^3+'x^2-'x-1)); a(n) = vecsum(Vec(lift(p^(n-1)))); \\ Kevin Ryde, May 02 2021

Crossrefs

Sequence in context: A035362 A042957 A341074 * A264870 A346048 A131048

Adjacent sequences: A343882 A343883 A343884 * A343886 A343887 A343888

Keyword

nonn,easy

Author

Zachary Gaiski, May 02 2021

Status

approved