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A071285
Numerators of Peirce sequence of order 5.
0
0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 3, 2, 3, 4, 2, 4, 5, 3, 1, 6, 5, 4, 7, 6, 3, 8, 5, 7, 9, 4, 8, 10, 6, 2, 11, 9, 7, 12, 10, 5, 13, 8, 11, 14, 6, 12, 15, 9, 3, 16, 13, 10, 17, 14, 7, 18, 11, 15, 19, 8, 16, 20, 12, 4, 21, 17, 13, 22, 18, 9, 23, 14, 19, 24, 10, 20, 25, 15, 5
OFFSET
0,9
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, p. 151.
FORMULA
Conjectures from Colin Barker, Mar 29 2017: (Start)
G.f.: x^5*(x^29 + x^28 + x^27 + 2*x^26 + x^25 + 2*x^24 + 3*x^23 + 2*x^22 + 3*x^21 + 4*x^20 + x^19 + 3*x^18 + 5*x^17 + 4*x^16 + 2*x^15 + 4*x^14 + 3*x^13 + 2*x^12 + 3*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + x^5)/(x^30 - 2*x^15 + 1).
a(n) = 2*a(n-15) - a(n-30) for n>29.
(End)
EXAMPLE
The Peirce sequences of orders 1, 2, 3, 4, 5 begin:
0/1 1/1 2/1 3/1 4/1 5/1 6/1 7/1 ...
0/2 0/1 1/2 2/2 1/1 3/2 4/2 2/1 ... (numerators are A009947)
0/2 0/3 0/1 1/3 1/2 2/3 2/2 3/3 ...
0/2 0/4 0/3 0/1 1/4 1/3 2/4 1/2 ...
0/2 0/4 0/5 0/3 0/1 1/5 1/4 1/3 ...
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
N. J. A. Sloane, Jun 11 2002
EXTENSIONS
Corrected and extended by Reiner Martin, Oct 15 2002
STATUS
approved