A124369 - OEIS

%I #6 Jan 22 2014 17:54:33

%S 1,0,1,1,1,1,2,2,2,1,2,6,4,3,1,4,9,12,7,4,1,7,17,24,21,11,5,1,10,34,

%T 48,50,34,16,6,1,17,58,103,110,91,52,22,7,1,28,104,200,250,220,152,76,

%U 29,8,1,44,188,385,534,530,400,239,107,37,9,1

%N Riordan array (1/((1-x-x^2)(1+x+x^2)),x(1+x)/((1-x-x^2)(1+x+x^2))).

%C Row sums are A123392. Diagonal sums are A124370. First column is A094686. Product of A026729 and abs(A049310).

%F Number triangle T(n,k)=sum{j=0..n, C(j,n-j)*C((j+k)/2,(j-k)/2)*(1+(-1)^(j-k))/2};

%F T(n,k) = T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + 2*T(n-3,k) + T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Jan 22 2014

%e Triangle begins

%e 1,

%e 0, 1,

%e 1, 1, 1,

%e 2, 2, 2, 1,

%e 2, 6, 4, 3, 1,

%e 4, 9, 12, 7, 4, 1,

%e 7, 17, 24, 21, 11, 5, 1,

%e 10, 34, 48, 50, 34, 16, 6, 1,

%e 17, 58, 103, 110, 91, 52, 22, 7, 1

%K easy,nonn,tabl

%O 0,7

%A _Paul Barry_, Oct 27 2006