A244629 - OEIS

%I #9 Apr 28 2019 18:24:32

%S 1,3,7,17,37,79,163,321,617,1179,2047,3761,6773,12103,20723,36733,

%T 62881,110231,186379

%N Number of power series 1 + c_1*x^1 + c_2*x^2 + ... + c_{n-1}*x^{n-1} + O(x^n) with c_k in {-1, 0, 1} whose reciprocal has the same property.

%C a(n) is odd since taking the reciprocal is an involution with only one fixed point.

%e a(3) = 7 since 1 / (1 +- x - x^2 + O(x^3)) = 1 -+ x + 2*x^2 + O(x^3) are excluded, but the other 7 power series 1 + c_1*x^1 + c_2^x^2 + O(x^3) have the property.

%o (PARI) {a(n) = my(c); if( n<1, 0, forvec( v = vector(n, i, [(-1)^(i>1), 1]), if( 1 >= vecmax( abs( Vec( 1 / Ser(v)))), c++)); c)};

%K nonn,more

%O 1,2

%A _Michael Somos_, Jul 02 2014