A085015 Multiplicity of the root 1 in the characteristic polynomial mod 2 of the n X n matrix with entries binomial(i+j,i), 0<=i,j

0, 1, 0, 3, 2, 5, 0, 3, 2, 5, 0, 11, 6, 9, 4, 7, 6, 9, 4, 15, 10, 21, 0, 11, 6, 9, 4, 15, 10, 13, 8, 11, 10, 13, 8, 19, 14, 25, 4, 15, 10, 21, 0, 43, 22, 33, 12, 23, 18, 21, 16, 27, 22, 33, 12, 23, 18, 21, 16, 27, 22, 25, 20, 23, 22, 25, 20, 31, 26, 37, 16, 27, 22, 33, 12, 55, 34, 45

Offset: 0

Author

Roland Bacher, Jun 18 2003

Keywords

• easy
• nonn

References

• R. Bacher and R. Chapman, Symmetric Pascal matrices modulo p, European J. Combin. 25 (2004), no. 4, 459-473.

Programs

Maple

f := (l,n)->if 2^l<(n) then f(l+1,n); else l fi; fo := n->f(0,n); a := n->if n=0 then 0 else (2^fo(n)+2*(-1)^fo(n))/3-(2^fo(n)-n)+2*a(2^fo(n)-n); fi;

Formula

a(0)=0 and a(2^l-k)=(2^l+2*(-1)^l)/3-k+2*a(k) for 0<=k<=2^(l-1).