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A115512 Number triangle (1,x)+(x,x^3) expressed in terms of Riordan arrays. 1

%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

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Last modified July 25 10:46 EDT 2021. Contains 346289 sequences. (Running on oeis4.)