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A270572 a(1)=3; thereafter a(n) is the number of occurrences of a(n-1) in {a(1), ... , a(n-1)}. 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 (list; graph; refs; listen; history; text; internal format)
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)*(r-1)+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(n-2)+a(n-6)-a(n-8) for n>9.

G.f.: x*(3+x-2*x^2+x^3+x^5-2*x^6-2*x^7+3*x^8+x^10-3*x^11-x^12+2*x^13-x^14) / ((1-x)^2*(1+x)^2*(1-x+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+x-2*x^2+x^3+x^5-2*x^6-2*x^7+3*x^8+x^10-3*x^11-x^12+2*x^13-x^14) / ((1-x)^2*(1+x)^2*(1-x+x^2)*(1+x+x^2)) + O(x^100)) \\ Colin Barker, Mar 20 2016

CROSSREFS

Cf. A181391, A267794, A268584, A269625.

Sequence in context: A107297 A107296 A080847 * A095276 A246457 A089338

Adjacent sequences:  A270569 A270570 A270571 * A270573 A270574 A270575

KEYWORD

nonn,easy

AUTHOR

Ctibor O. Zizka, Mar 19 2016

STATUS

approved

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Last modified September 20 12:31 EDT 2017. Contains 292271 sequences.