A244629 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.

1, 3, 7, 17, 37, 79, 163, 321, 617, 1179, 2047, 3761, 6773, 12103, 20723, 36733, 62881, 110231, 186379

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..19.

Example

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.

Prog

(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)};

Crossrefs

Sequence in context: A354124 A089099 A089116 * A065545 A110930 A026646

Adjacent sequences: A244626 A244627 A244628 * A244630 A244631 A244632

Keyword

nonn,more

Author

Michael Somos, Jul 02 2014

Status

approved