OFFSET
0,8
COMMENTS
Sum of terms in row 2n (n>=1) is 0. Sum of the absolute values of the terms in row 2n is C(2n,n) (A000984). All terms in row 2n-1 are nonpositive. Their sum is -4^(n-1). M(2n-1)S(2n-1)=-S(2n-1)
EXAMPLE
M(4)=[0,1,1,1/1,0,1,1/1,1,0,1/1,1,1,0], S(4)=[0,1,-1,1/-1,0,1,-1/1,-1,0,1/-1,1,-1,0], M(4)S(4)=[ -1,0,0,0/0,1,-2,2/-2,2,-1,0/0,0,0,1]; char. poly. of M(4)S(4) is x^4 + 2x^2 - 3, yielding row 4 of the triangle: -3,0,2,0,1.
Triangle starts:
1;
0,-1;
-1,0,1;
0,-3,0,-1;
-3,0,2,0,1;
0,-5,0,-10,0,-1
MAPLE
with(linalg): m:=proc(i, j) if i=j then 0 else 1 fi end: s:=proc(i, j) if i=j then 0 elif i>j then (-1)^(i+j) else (-1)^(i+j+1) fi end: for n from 1 to 14 do f[n]:=(-1)^n*sort(expand(charpoly(multiply(matrix(n, n, m), matrix(n, n, s)), x))) od: 1; for n from 1 to 14 do seq(coeff(f[n], x, j), j=0..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Jan 01 2007
EXTENSIONS
Edited by N. J. A. Sloane, Jan 07 2006
STATUS
approved