A071287 Numerators of Peirce sequence of order 6.

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 3, 1, 3, 4, 2, 3, 4, 5, 2, 4, 6, 5, 3, 1, 7, 6, 5, 8, 4, 7, 6, 9, 3, 8, 10, 5, 7, 9, 11, 4, 8, 12, 10, 6, 2, 13, 11, 9, 14, 7, 12, 10, 15, 5, 13, 16, 8, 11, 14, 17, 6, 12, 18, 15, 9, 3, 19, 16, 13, 20, 10, 17, 14, 21, 7, 18, 22

Offset

0,10

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..79.

Formula

Conjectures from Colin Barker, Mar 29 2017: (Start)

G.f.: x^6*(x^41 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^36 + x^35 + 3*x^34 + 2*x^33 + 3*x^32 + 2*x^31 + 4*x^30 + 3*x^29 + 4*x^28 + 5*x^27 + x^26 + 3*x^25 + 5*x^24 + 6*x^23 + 4*x^22 + 2*x^21 + 5*x^20 + 4*x^19 + 3*x^18 + 2*x^17 + 4*x^16 + 3*x^15 + x^14 + 3*x^13 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + x^8 + x^7 + x^6)/(x^42 - 2*x^21 + 1).

a(n) = 2*a(n-21) - a(n-42) for n>41.

(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. A071281-A071288.

Sequence in context: A024160 A295283 A103284 * A355731 A353394 A349494

Adjacent sequences: A071284 A071285 A071286 * A071288 A071289 A071290

Keyword

nonn,frac,easy

Author

N. J. A. Sloane, Jun 11 2002

Extensions

More terms from Reiner Martin, Oct 15 2002

Status

approved