%I #2 Mar 30 2012 17:28:32

%S 1,2,1,3,2,1,6,6,4,1,10,12,12,4,1,20,30,36,18,6,1,36,62,92,56,27,6,1,

%T 72,144,246,188,110,36,8,1,136,304,600,536,380,152,48,8,1,272,680,

%U 1504,1576,1296,644,248,60,10,1,528,1448,3576,4256,4008,2332,1080,320,75,10

%N Triangle T, read by rows, equal to the matrix square of Losanitsch's triangle (A034851).

%C Conjectures: (1) The first column equals the row sums of Losanitsch's triangle (which equals A005418). (2) Let L^n denote the n-th power of Losanitsch's triangle. Then the first column of L^(n+1) equals the row sums of L^n.

%o (PARI) s=13;L=matrix(s,s); T(n, k)= (1/2) *(binomial(n, k)+binomial(n%2, k%2)*binomial(n\2, k\2)); for(n=1,s,for(k=1,s,L[n,k]=T(n-1,k-1))); L2=L*L; for(n=1,s,for(k=1,n,print1(L2[n,k],", ")));

%Y Cf. A034851, A005418.

%K easy,nonn,tabl

%O 0,2

%A _Gerald McGarvey_, Oct 30 2007