

A187182


Parse the infinite string 0123012301230123... into distinct phrases 0, 1, 2, 3, 01, 23, 012, ...; a(n) = length of nth phrase.


2



1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 6, 7, 6, 6, 7, 7, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 10, 11, 10, 10, 11, 11, 11, 12, 13, 12, 13, 12, 13, 12, 13, 14, 14, 15, 14, 14, 15, 15, 15, 16, 17, 16, 17, 16, 17, 16, 17, 18, 18, 19, 18, 18, 19, 19, 19, 20, 21, 20, 21, 20, 21, 20, 21, 22, 22, 23, 22, 22, 23, 23, 23, 24, 25, 24, 25, 24, 25, 24, 25
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OFFSET

1,5


COMMENTS



LINKS

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1).


FORMULA

G.f.: x*(1 + x^4 + x^6  x^7 + x^9 + x^12 + x^13  x^14 + x^15  2*x^16 + x^17  x^18 + x^19) / ((1  x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)).
a(n) = a(n1) + a(n16)  a(n17) for n>20.
(End)


EXAMPLE

The sequence is quasiperiodic with period 16, increasing by 4 after each block:
1 1 1 1
2 2 3 2 2 3 3 3 4 5 4 5 4 5 4 5
6 6 7 6 6 7 7 7 8 9 8 9 8 9 8 9
10 10 11 10 10 11 11 11 12 13 12 13 12 13 12 13
14 14 15 14 14 15 15 15 16 17 16 17 16 17 16 17
...


MATHEMATICA

Join[{1, 1, 1}, LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}, {1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5}, 97]] (* Ray Chandler, Aug 26 2015 *)


PROG

(PARI) Vec(x*(1 + x^4 + x^6  x^7 + x^9 + x^12 + x^13  x^14 + x^15  2*x^16 + x^17  x^18 + x^19) / ((1  x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)) + O(x^80)) \\ Colin Barker, Jan 31 2020


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



