A302130 a(n) = a(a(n-3)) + a(n-a(n-2)) with a(1) = a(2) = a(3) = a(4) = 1, a(5) = 2, a(6) = 5.

1, 1, 1, 1, 2, 5, 3, 2, 7, 3, 2, 10, 3, 2, 13, 3, 2, 16, 3, 2, 19, 3, 2, 22, 3, 2, 25, 3, 2, 28, 3, 2, 31, 3, 2, 34, 3, 2, 37, 3, 2, 40, 3, 2, 43, 3, 2, 46, 3, 2, 49, 3, 2, 52, 3, 2, 55, 3, 2, 58, 3, 2, 61, 3, 2, 64, 3, 2, 67, 3, 2, 70, 3, 2, 73, 3, 2, 76, 3, 2, 79, 3, 2, 82, 3, 2, 85, 3, 2, 88

Offset: 1

Author

Altug Alkan, Jun 20 2018

Keywords

• nonn
• easy

Comments

A quasi-periodic solution to the recurrence a(n) = a(a(n-3)) + a(n-a(n-2)).

Examples

			a(3*k-2) = 3, a(3*k-1) = 2, a(3*k) = 3*k - 2 for k > 2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A244477.

Programs

GAP

a:=[1,1,1,1,2,5];; for n in [7..100] do a[n]:=a[a[n-3]]+a[n-a[n-2]]; od; a; # Muniru A Asiru, Jun 26 2018

Mathematica

LinearRecurrence[{0,0,2,0,0,-1},{1,1,1,1,2,5,3,2,7,3,2,10},100] (* Harvey P. Dale, Apr 20 2022 *)

PARI

a=vector(99); a[1]=a[2]=a[3]=a[4]=1;a[5]=2;a[6]=5;for(n=7, #a, a[n] = a[a[n-3]]+a[n-a[n-2]]); a

PARI

Vec(x*(1 + x + x^2 - x^3 + 3*x^5 + 2*x^6 - x^7 - 2*x^8 - 2*x^9 + x^11) / ((1 - x)^2*(1 + x + x^2)^2) + O(x^80)) \\ Colin Barker, Jun 20 2018

Formula

From Colin Barker, Jun 20 2018: (Start)

G.f.: x*(1 + x + x^2 - x^3 + 3*x^5 + 2*x^6 - x^7 - 2*x^8 - 2*x^9 + x^11) / ((1 - x)^2*(1 + x + x^2)^2).

a(n) = 2*a(n-3) - a(n-6) for n>10.

(End)