A132158 a(3n+k) = 3a(3n+k-1)-3a(3n+k-2)+2a(3n+k-3) for k = 0,1; a(3n+2) = 3a(3n-1)-3a(3n-2), with a(0) = 0,a(1) = 1,a(2) = 3.

0, 1, 3, 6, 11, 15, 24, 49, 75, 126, 251, 375, 624, 1249, 1875, 3126, 6251, 9375

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (1, -1, 5, -5, 5).

Formula

Sequence is identical to its third differences in absolute values.

G.f.:-x*(x+1)*(3*x^2+x+1)/((x^2-x+1)*(5*x^3-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]

Mathematica

LinearRecurrence[{1, -1, 5, -5, 5}, {0, 1, 3, 6, 11}, 18] (* Ray Chandler, Sep 23 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 5, -5, 5, -1, 1]^n*[0; 1; 3; 6; 11])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Sequence in context: A256001 A131665 A363610 * A363644 A363652 A368586

Adjacent sequences: A132155 A132156 A132157 * A132159 A132160 A132161

Keyword

nonn,easy,changed

Author

Paul Curtz, Nov 02 2007

Status

approved