0,2

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to Stern's sequences

E.g.f.: exp(asinh(x))((1+x)/(1+x^2)+(2-x+x^2)/(1+x^2)^(3/2))-2. - Michael Somos Mar 11 2004

b[ n_ ] := 2-(-1)^n; a[ 1 ] := -1; a[ n_Integer?EvenQ ] := -n(n+1); a[ n_Integer?OddQ ] := -(n-2)(n-1); then use the standard algorithm to get p[ n ]/q[ n ].

(PARI) a(n)=if(n<0, 0, prod(k=1, n, if(k%2, k+2, 1-k)))

(PARI) {a(n)=local(A); if(n<0, 0, A=matrix(2, n+1); for(k=0, n, A[2, k+1]=if(k%2, 3, 1); A[1, k+1]=if(k<2, (-1)^k, if(k%2, -(k-2)*(k-1), -k*(k+1)))); contfracpnqn(A)[2, 1])} /* Michael Somos Jul 15 2003 */

Numerators p[ n ] are (-1)^[n/2]*A001900(n). See also A013069.

Cf. A079484.

Sequence in context: A046983 A067655 A049606 this_sequence A143257 A089403 A111674

Adjacent sequences: A046123 A046124 A046125 this_sequence A046127 A046128 A046129

sign,frac

Eric Weisstein (eric(AT)weisstein.com)