

A071283


Numerators of Peirce sequence of order 4.


0



0, 0, 0, 0, 1, 1, 2, 1, 2, 3, 2, 4, 3, 1, 5, 4, 6, 3, 5, 7, 4, 8, 6, 2, 9, 7, 10, 5, 8, 11, 6, 12, 9, 3, 13, 10, 14, 7, 11, 15, 8, 16, 12, 4, 17, 13, 18, 9, 14, 19, 10, 20, 15, 5, 21, 16, 22, 11, 17, 23, 12, 24, 18, 6, 25, 19, 26, 13, 20, 27, 14, 28, 21, 7, 29, 22, 30, 15, 23, 31
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OFFSET

0,7


REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, AddisonWesley, 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^4*(x^19 + x^18 + x^17 + 2*x^16 + 2*x^15 + 3*x^14 + x^13 + 3*x^12 + 4*x^11 + 2*x^10 + 3*x^9 + 2*x^8 + x^7 + 2*x^6 + x^5 + x^4)/(x^20  2*x^10 + 1).
a(n) = 2*a(n10)  a(n20) for n>19.
(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. A071281A071288.
Sequence in context: A302098 A112779 A029201 * A172986 A029826 A192185
Adjacent sequences: A071280 A071281 A071282 * A071284 A071285 A071286


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



