A181653 - OEIS

A181653

Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x) if k mod 2 = 0, x^k*(1+x+x^2) otherwise.

%I #5 Sep 29 2018 18:47:26

%S 1,1,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,

%T 1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,1

%N Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x) if k mod 2 = 0, x^k*(1+x+x^2) otherwise.

%C Row sums are A174296. A181654 is an eigentriangle.

%e Triangle begins

%e 1;

%e 1, 1;

%e 0, 1, 1;

%e 0, 1, 1, 1;

%e 0, 0, 0, 1, 1;

%e 0, 0, 0, 1, 1, 1;

%e 0, 0, 0, 0, 0, 1, 1;

%e 0, 0, 0, 0, 0, 1, 1, 1;

%e 0, 0, 0, 0, 0, 0, 0, 1, 1;

%e 0, 0, 0, 0, 0, 0, 0, 1, 1, 1;

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1;

%e Production matrix begins

%e 1, 1;

%e -1, 0, 1;

%e 1, 1, 0, 1;

%e 0, -1, -1, 0, 1;

%e 0, 1, 1, 1, 0, 1;

%e 0, 0, 0, -1, -1, 0, 1;

%e 0, 0, 0, 1, 1, 1, 0, 1;

%e 0, 0, 0, 0, 0, -1, -1, 0, 1;

%e 0, 0, 0, 0, 0, 1, 1, 1, 0, 1;

%e 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1;

%K easy,nonn,tabl

%O 0,1

%A _Paul Barry_, Nov 03 2010