Mike Stay wrote On Wed, Sep 20, 2017 at 6:06 PM, Bill Gosper <billgosper@gmail.com> wrote: http://mathworld.wolfram.com/Thue-MorseSequence.html gives (if simplified) ThueMorse@n == Mod[3^n*Binomial[1/2, n]*Hypergeometric2F1[3/2, -n, 3/2 - n, -1/3]/2 - 1/2,2] HtF? --rwg Amazing: In[599]:= Series[(1+Sqrt[(1-3x)/(1+x)])/(2(1+x)),{x,0,33}] Out[599]= 1-2 x+2 x^2-3 x^3+2 x^4-5 x^5-x^6-14 x^7-22 x^8-69 x^9-163 x^10-440 x^11-1145 x^12-3068 x^13-8230 x^14-22307 x^15-60790 x^16-166685 x^17-459307 x^18-1271480 x^19-3534115 x^20-9859574 x^21-27598756 x^22-77490473 x^23-218183521 x^24-615902900 x^25-1742738476 x^26-4942022649 x^27-14043034702 x^28-39979680749 x^29-114020882009 x^30-325721340062 x^31-931921909078 x^32-2670196518173 x^33+O[x]^34 In[600]:= Mod[CoefficientList[%,x],2] Out[600]= {1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1} I notice that SeriesCoefficient boggles here instead of finding the 2F1. I wonder how SW got it. --rwg -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com