This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086215 Number of (-1,0,1) n X n matrices M that are positive definite. 3
 1, 7, 311, 79505, 105311665, 642005451319, 15477341239385927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS M need not be symmetric. For the number of different values of M + M' see A114601. - Max Alekseyev, Dec 13 2005 LINKS Eric Weisstein's World of Mathematics, Positive Definite Matrix PROG (PARI) { a(n) = M=matrix(n, n, i, j, 2*(i==j)); r=0; b(1); r } { b(k) = local(z, t); if(k>n, z=t=0; for(i=1, n, for(j=1, i-1, if(M[ i, j ]==0, z++); if(abs(M[ i, j ])==1, t++); )); r+=3^z*2^t; return; ); forvec(x=vector(k-1, i, [ -1, 1 ]), for(i=1, k-1, M[ k, i ]=M[ i, k ]=x[ i ]); if( matdet(vecextract(M, 2^k-1, 2^k-1), 1)>0, b(k+1) ) ) } /* Max Alekseyev */ CROSSREFS Cf. A114601, A085656. Sequence in context: A002437 A300870 A239163 * A119163 A171148 A219267 Adjacent sequences:  A086212 A086213 A086214 * A086216 A086217 A086218 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 12 2003 EXTENSIONS a(4) from Wouter Meeussen, Sep 05 2003 a(5)-a(6) from Max Alekseyev, Dec 13 2005 a(7) from Max Alekseyev, Nov 09 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 01:33 EST 2019. Contains 329978 sequences. (Running on oeis4.)