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A071287 Numerators of Peirce sequence of order 6. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A072084 A336471 A133755

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 (reinermartin(AT)hotmail.com), Oct 15 2002

STATUS

approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)