A140298 a(0)=1; a(3n+1) = a(3n)+1, a(3n+2) = a(3n+1) + a(3n) (=3*A000244), a(3n+3) = a(3n+2) + a(3n) (=A003462(n+2)).

1, 2, 3, 4, 5, 9, 13, 14, 27, 40, 41, 81, 121, 122, 243, 364, 365, 729, 1093, 1094, 2187, 3280, 3281, 6561, 9841, 9842, 19683, 29524, 29525, 59049, 88573, 88574, 177147, 265720, 265721, 531441, 797161, 797162, 1594323, 2391484, 2391485, 4782969, 7174453, 7174454

Offset: 0

Author

Paul Curtz, May 25 2008

Keywords

• nonn
• easy

Comments

Note period 12 for a(n) mod 10.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (-1,-1,3,3,3)

Crossrefs

Cf. A107365.

Programs

PARI

Vec((1+3*x+6*x^2+6*x^3+3*x^4)/((1+x+x^2)*(1-3*x^3))+O(x^99)) \\ Charles R Greathouse IV, Jun 20 2011

Formula

From R. J. Mathar, Jan 17 2009: (Start)

G.f.: (1 + 3*x + 6*x^2 + 6*x^3 + 3*x^4)/((1 + x + x^2)*(1 - 3*x^3)).

a(n) = -a(n-1) - a(n-2) + 3*a(n-3) + 3*a(n-4) + 3*a(n-5).

a(n) = (3*b(n)-A049347(n))/2 where b(n)=1,1,2,3,3,6,9,9,18,27,27,54,.. = 3*b(n-3).

(End)

Extensions

a(27)-a(43) added by Andrew Howroyd, Nov 03 2018