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Numerators of Peirce sequence of order 4.
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%I #7 Oct 30 2022 18:19:59

%S 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,

%T 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,

%U 17,23,12,24,18,6,25,19,26,13,20,27,14,28,21,7,29,22,30,15,23,31

%N Numerators of Peirce sequence of order 4.

%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^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).

%F a(n) = 2*a(n-10) - a(n-20) for n>19.

%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 0,7

%A _N. J. A. Sloane_, Jun 11 2002

%E More terms from _Reiner Martin_, Oct 15 2002