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A156062 Riordan array (1/(1-x^4), x/(1-x^4)).

%I A156062 #2 Mar 30 2012 18:59:22
%S A156062 1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,2,0,0,0,1,0,0,3,0,0,0,1,0,0,0,4,0,0,
%T A156062 0,1,1,0,0,0,5,0,0,0,1,0,3,0,0,0,6,0,0,0,1,0,0,6,0,0,0,7,0,0,0,1,0,0,
%U A156062 0,10,0,0,0,8,0,0,0,1,1,0,0,0,15,0,0,0,9,0,0,0,1,0,4,0,0,0,21,0,0,0,10,0,0,0
%N A156062 Riordan array (1/(1-x^4), x/(1-x^4)).
%C A156062 Row sums are A003269(n+1). Diagonal sums are the aerated Fibonacci numbers; thus
%C A156062 F(n+1)=sum{k=0..n, C((n+k)/2,k)*(1+(-1)^(n-k))/2}. Inverse is A156064.
%F A156062 Triangle T(n,k)=C((n+3k)/4,k)((1+(-1)^(n-k))/2+cos(pi*(n-k)/2))/2.
%e A156062 Triangle begins
%e A156062 1,
%e A156062 0, 1,
%e A156062 0, 0, 1,
%e A156062 0, 0, 0, 1,
%e A156062 1, 0, 0, 0, 1,
%e A156062 0, 2, 0, 0, 0, 1,
%e A156062 0, 0, 3, 0, 0, 0, 1,
%e A156062 0, 0, 0, 4, 0, 0, 0, 1,
%e A156062 1, 0, 0, 0, 5, 0, 0, 0, 1,
%e A156062 0, 3, 0, 0, 0, 6, 0, 0, 0, 1,
%e A156062 0, 0, 6, 0, 0, 0, 7, 0, 0, 0, 1,
%e A156062 0, 0, 0, 10, 0, 0, 0, 8, 0, 0, 0, 1,
%e A156062 1, 0, 0, 0, 15, 0, 0, 0, 9, 0, 0, 0, 1
%e A156062 Production matrix of this array is
%e A156062 0, 1,
%e A156062 0, 0, 1,
%e A156062 0, 0, 0, 1,
%e A156062 1, 0, 0, 0, 1,
%e A156062 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 0, 0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
%e A156062 -91, 0, 0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1
%e A156062 where 1,1,-3,15,-91,612,.... is (-1)^(n-1)*C(4n-1,n)/(4n-1) (see A006632).
%K A156062 easy,nonn,tabl
%O A156062 0,17
%A A156062 _Paul Barry_, Oct 20 2009