A117316 - OEIS

%I #5 Jan 06 2014 05:55:21

%S 1,0,1,2,0,1,2,4,0,1,6,4,6,0,1,10,16,6,8,0,1,22,28,30,8,10,0,1,42,72,

%T 54,48,10,12,0,1,86,148,158,88,70,12,14,0,1,170,336,342,288,130,96,14,

%U 16,0,1,342,716,846,648,470,180,126,16,18,0,1

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

%C Product of A007318 and alternating sign version of A073370. Row sums are A001333. Diagonal sums are A052973. First column is A078008. Convolution array for A078008.

%F T(n,k)=sum{j=0..n-k,sum{i=0..k+1, C(k+1,i)C(k+j,j)C(n-i-j,n-k-i-j)(-1)^(i+j)2^(n-k-i-j)}}

%F T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k)-T(n-2,k-1), T(0,0)= 1, T(1,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - _Philippe Deléham_, Jan 04 2013

%e Triangle begins

%e 1,

%e 0, 1,

%e 2, 0, 1,

%e 2, 4, 0, 1,

%e 6, 4, 6, 0, 1,

%e 10, 16, 6, 8, 0, 1,

%e 22, 28, 30, 8, 10, 0, 1,

%e 42, 72, 54, 48, 10, 12, 0, 1

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Mar 07 2006