%I
%S 1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,
%T 0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,
%U 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1
%N Number triangle (1,x)+(x,x^3) expressed in terms of Riordan arrays.
%C Row sums are periodic {1,2,1}. Diagonal sums are periodic {1,1,1,0}. Inverse is A115513.
%F Column k has g.f. x^k+x^(3k+1); Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=3k+1, 1, 0).
%e Triangle begins
%e 1,
%e 1, 1,
%e 0, 0, 1,
%e 0, 0, 0, 1,
%e 0, 1, 0, 0, 1,
%e 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 1, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
%K easy,nonn,tabl
%O 0,1
%A _Paul Barry_, Jan 23 2006
