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%I #8 Oct 30 2022 18:19:59
%S 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,
%T 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,
%U 14,17,6,12,18,15,9,3,19,16,13,20,10,17,14,21,7,18,22
%N Numerators of Peirce sequence of order 6.
%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, p. 151.
%F Conjectures from _Colin Barker_, Mar 29 2017: (Start)
%F 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).
%F a(n) = 2*a(n-21) - a(n-42) for n>41.
%F (End)
%e The Peirce sequences of orders 1, 2, 3, 4, 5 begin:
%e 0/1 1/1 2/1 3/1 4/1 5/1 6/1 7/1 ...
%e 0/2 0/1 1/2 2/2 1/1 3/2 4/2 2/1 ... (numerators are A009947)
%e 0/2 0/3 0/1 1/3 1/2 2/3 2/2 3/3 ...
%e 0/2 0/4 0/3 0/1 1/4 1/3 2/4 1/2 ...
%e 0/2 0/4 0/5 0/3 0/1 1/5 1/4 1/3 ...
%Y Cf. A071281-A071288.
%K nonn,frac,easy
%O 0,10
%A _N. J. A. Sloane_, Jun 11 2002
%E More terms from _Reiner Martin_, Oct 15 2002
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