A275363 a(1)=3, a(2)=6, a(3)=3; thereafter a(n) = a(n-a(n-1)) + a(n-1-a(n-2)).

3, 6, 3, 3, 9, 6, 3, 12, 9, 3, 15, 12, 3, 18, 15, 3, 21, 18, 3, 24, 21, 3, 27, 24, 3, 30, 27, 3, 33, 30, 3, 36, 33, 3, 39, 36, 3, 42, 39, 3, 45, 42, 3, 48, 45, 3, 51, 48, 3, 54, 51, 3, 57, 54, 3, 60, 57, 3, 63, 60, 3, 66, 63, 3, 69, 66, 3, 72, 69

Offset: 1

Author

Nathan Fox, Jul 24 2016

Keywords

• nonn

Comments

Same recurrence as in A046699 but with different starting values.

This sequence is quasilinear.

Links

• Nathan Fox, Table of n, a(n) for n = 1..1000
• Nathan Fox, Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic Computation, arXiv:1609.06342 [math.NT], 2016.
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A046699, A005185, A244477.

Programs

Mathematica

Flatten[Array[{3, 3*# + 6, 3*# + 3} &, 30, 0]] (* Paolo Xausa, Oct 23 2024 *)
LinearRecurrence[{0,0,2,0,0,-1},{3,6,3,3,9,6},80] (* Harvey P. Dale, Nov 27 2024 *)

Formula

a(3n) = 3n, a(3n+1) = 3, a(3n+2) = 3n+6.

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

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