

A270572


a(1)=3; thereafter a(n) is the number of occurrences of a(n1) in {a(1), ... , a(n1)}.


1



3, 1, 1, 2, 1, 3, 2, 2, 3, 3, 4, 1, 4, 2, 4, 3, 5, 1, 5, 2, 5, 3, 6, 1, 6, 2, 6, 3, 7, 1, 7, 2, 7, 3, 8, 1, 8, 2, 8, 3, 9, 1, 9, 2, 9, 3, 10, 1, 10, 2, 10, 3, 11, 1, 11, 2, 11, 3, 12, 1, 12, 2, 12, 3, 13, 1, 13, 2, 13, 3, 14, 1, 14, 2, 14, 3, 15, 1, 15, 2, 15, 3, 16, 1, 16, 2, 16, 3, 17, 1, 17, 2, 17, 3, 18, 1, 18, 2, 18, 3, 19, 1
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OFFSET

1,1


COMMENTS

For a(1)=3 the members of the sequence from a(12) onwards are of the form a(6*r+6)=1, a(6*r+7)=3+r, a(6*r+8)=2, a(6*r+9)=3+r, a(6*r+10)=3, a(6*r+11)=4+r, r>=1.
For every integer a(1)>=1, from a(a(1)*a(1)+3) onwards, the members of the sequence are of the form a(n)=1, a(n+1)=a(1)+r, a(n+2)=2, a(n+3)=a(1)+r, ... , a(n+2*a(1)2)=a(1), a(n+2*a(1)1)=a(1)+r+1. n = a(1)*a(1)+2*a(1)*(r1)+3, r>=1.


LINKS

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


FORMULA

From Colin Barker, Mar 20 2016: (Start)
a(n) = a(n2)+a(n6)a(n8) for n>9.
G.f.: x*(3+x2*x^2+x^3+x^52*x^62*x^7+3*x^8+x^103*x^11x^12+2*x^13x^14) / ((1x)^2*(1+x)^2*(1x+x^2)*(1+x+x^2)).
(End)


EXAMPLE

a(1)=3. The number of occurrences of 3 in {3} is 1, thus a(2)=1. The number of occurrences of 1 in {3,1} is 1, thus a(3)=1. The number of occurrences of 1 in {3, 1, 1} is 2, thus a(4)=2. The number of occurrences of 2 in {3, 1, 1, 2} is 1, thus a(5)=1. The number of occurrences of 1 in {3, 1, 1, 2, 1} is 3, thus a(6)=3 , and so on.


PROG

(PARI) Vec(x*(3+x2*x^2+x^3+x^52*x^62*x^7+3*x^8+x^103*x^11x^12+2*x^13x^14) / ((1x)^2*(1+x)^2*(1x+x^2)*(1+x+x^2)) + O(x^100)) \\ Colin Barker, Mar 20 2016


CROSSREFS

Cf. A181391, A267794, A268584, A269625.
Sequence in context: A107296 A080847 A326406 * A095276 A246457 A089338
Adjacent sequences: A270569 A270570 A270571 * A270573 A270574 A270575


KEYWORD

nonn,easy


AUTHOR

Ctibor O. Zizka, Mar 19 2016


STATUS

approved



