A193527 G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u * (u - 2) - (v + 2).

1, 1, 2, 0, -1, 0, 2, 0, -5, 0, 12, 0, -30, 0, 82, 0, -233, 0, 668, 0, -1949, 0, 5802, 0, -17503, 0, 53302, 0, -163783, 0, 507418, 0, -1582869, 0, 4966790, 0, -15667573, 0, 49658264, 0, -158059506, 0, 505013014, 0, -1619144976, 0, 5207596574

Offset

-1,3

Links

Table of n, a(n) for n=-1..45.

Formula

a(2*n) = 0 unless n=0. a(n) = A107088(n+1) unless n=0. a(2*n - 1) = A107087(n).

Example

1/x + 1 + 2*x - x^3 + 2*x^5 - 5*x^7 + 12*x^9 - 30*x^11 + 82*x^13 - ...

Prog

(PARI) {a(n) = local(A, m); if( n<-1, 0, if( n%2 == 0, n==0, A = 1 + O(x); m=1; while( 2*m <= n+1, A = sqrt(4*x + subst(A, x, x^2)); m*=2); polcoeff(A, (n+1)/2)))}

Crossrefs

Cf. A107087, A107088.

Sequence in context: A110914 A219200 A341978 * A127505 A194923 A321103

Adjacent sequences: A193524 A193525 A193526 * A193528 A193529 A193530

Keyword

sign

Author

Michael Somos, Aug 04 2011

Status

approved