cp's OEIS Frontend

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

%I A085015 #6 Mar 31 2012 10:22:38
%S A085015 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,
%T A085015 8,11,10,13,8,19,14,25,4,15,10,21,0,43,22,33,12,23,18,21,16,27,22,33,
%U A085015 12,23,18,21,16,27,22,25,20,23,22,25,20,31,26,37,16,27,22,33,12,55,34,45
%N 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<n.
%D A085015 R. Bacher and R. Chapman, Symmetric Pascal matrices modulo p, European J. Combin. 25 (2004), no. 4, 459-473.
%F A085015 a(0)=0 and a(2^l-k)=(2^l+2*(-1)^l)/3-k+2*a(k) for 0<=k<=2^(l-1).
%p A085015 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;
%K A085015 easy,nonn
%O A085015 0,4
%A A085015 _Roland Bacher_, Jun 18 2003