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A085657
Number of n X n symmetric positive definite matrices with 2's on the main diagonal and 1's and 0's elsewhere.
6
1, 2, 8, 61, 819, 17417, 506609, 15582436
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OFFSET
1,2
COMMENTS
Of course the total number of symmetric matrices of this type (not necessarily positive definite) is 2^C(n,2).
This gives the number of different values of A + A' where A runs through the matrices counted in
A085656
. -
Max Alekseyev
, Dec 13 2005
LINKS
Table of n, a(n) for n=1..8.
Index entries for sequences related to binary matrices
EXAMPLE
The singular matrix
2 0 1 1
0 2 1 1
1 1 2 0
1 1 0 2
is one of the three 4 X 4 matrices which are not positive definite.
PROG
(PARI) { a(n) = M=matrix(n, n, i, j, 2*(i==j)); r=0; b(1); r } { b(k) = if(k>n, r++; return); forvec(x=vector(k-1, i, [0, 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.
A085659
,
A080858
,
A083029
.
Cf.
A085656
,
A114601
.
Sequence in context:
A370913
A208356
A188489
*
A005215
A058862
A191482
Adjacent sequences:
A085654
A085655
A085656
*
A085658
A085659
A085660
KEYWORD
nonn
AUTHOR
N. J. A. Sloane
, Jul 12 2003
EXTENSIONS
More terms from
Max Alekseyev
, Dec 13 2005
STATUS
approved
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Last modified March 18 22:24 EDT 2024. Contains 370951 sequences. (Running on oeis4.)