A071281 Numerators of Peirce sequence of order 3.

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

Author

N. J. A. Sloane, Jun 11 2002

Keywords

• nonn
• frac
• easy

Examples

			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 ...
		

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, p. 151.

Crossrefs

Cf. A071282-A071288.

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)

Extensions

More terms from Reiner Martin, Oct 15 2002