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

0,6

References

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

Links

Table of n, a(n) for n=0..77.

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

Cf. A071282-A071288.

Sequence in context: A303777 A366749 A304529 * A361249 A204995 A371907

Adjacent sequences: A071278 A071279 A071280 * A071282 A071283 A071284

Keyword

nonn,frac,easy

Author

N. J. A. Sloane, Jun 11 2002

Extensions

More terms from Reiner Martin, Oct 15 2002

Status

approved