A274768 - OEIS

A274768

Lexicographically earliest increasing sequence a, b, c, ... such that every partial product (1-x^a), (1-x^a)(1-x^b), (1-x^a)(1-x^b)(1-x^c), ... has coefficients -1, 0, 1 only.

%I #13 Nov 14 2016 11:09:25

%S 1,2,3,5,7,8,9,17,26,43,46,60,175,221,396,617,1013,1630,2643,4273,

%T 6916,11189,18105,29294,47399,76693,124092,200785,324877,525662,

%U 850539,1376201,2226740,3602941,5829681,9432622,15262303,24694925,39957228,64652153,104609381

%N Lexicographically earliest increasing sequence a, b, c, ... such that every partial product (1-x^a), (1-x^a)(1-x^b), (1-x^a)(1-x^b)(1-x^c), ... has coefficients -1, 0, 1 only.

%F Empirical g.f.: x*(1 + x - x^4 - 4*x^5 - 6*x^6 - 23*x^10 - 29*x^11 + 69*x^12 - 14*x^13) / (1 - x - x^2). - _Colin Barker_, Nov 13 2016

%e a(4) = 5 because (1-x), (1-x)(1-x^2), and (1-x)(1-x^2)(1-x^3)(1-x^5) all have coefficients -1, 0, 1, but (1-x)(1-x^2)(1-x^3)(1-x^4) doesn't.

%K nonn

%O 1,2

%A _Jeffrey Shallit_, Jul 05 2016

%E a(19)-a(41) from _Jon E. Schoenfield_, Nov 12 2016