%I #16 Jul 25 2017 20:15:21

%S 1,1,3,-3,3,15,-57,21,867,-1893,1581,8283,-76953,34203,361551,-869691,

%T 6420387,34130067,-167946159,79445631,1696170093,-4239570255,

%U 4083041217,21859150803,-442212416121,215805655695,2316081934929,-5909439428697,11656013746863,62663656767603,-322045194694305,160129270032933,27589357112530467

%N Numerators of coefficients in Taylor series expansion of (1+x+x^2)^(1/2).

%C Denominators of the Taylor series expansion are given by A046161.

%C The terms after the second are divisible by 3.

%C The sequence of the absolute values is not monotonic.

%p a:= n-> numer(coeff(series(sqrt(1+x+x^2), x, n+3), x, n)):

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jul 25 2017

%t Numerator[CoefficientList[Series[Sqrt[1+x+x^2], {x, 0, 32}], x]]

%o (PARI) x = 'x + O('x^40); apply(x->numerator(x), Vec((1+x+x^2)^(1/2))) \\ _Michel Marcus_, Jul 24 2017

%Y Cf. A046161 (denominators).

%K sign,frac

%O 0,3

%A _Bruno Zürcher_, Jul 22 2017