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A071281
Numerators of Peirce sequence of order 3.
8
0, 0, 0, 1, 1, 2, 2, 3, 1, 4, 3, 5, 4, 6, 2, 7, 5, 8, 6, 9, 3, 10, 7, 11, 8, 12, 4, 13, 9, 14, 10, 15, 5, 16, 11, 17, 12, 18, 6, 19, 13, 20, 14, 21, 7, 22, 15, 23, 16, 24, 8, 25, 17, 26, 18, 27, 9, 28, 19, 29, 20, 30, 10, 31, 21, 32, 22, 33, 11, 34, 23, 35, 24, 36, 12, 37, 25, 38
OFFSET
0,6
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^3*(x^11 + x^10 + 2*x^9 + x^8 + 3*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3)/(x^12 - 2*x^6 + 1).
a(n) = 2*a(n-6) - a(n-12) for n>11.
(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
More terms from Reiner Martin, Oct 15 2002
STATUS
approved