A117316 Riordan array ((1-x)/(1-x-2x^2),x(1-x)/(1-x-2x^2)).

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, 54, 48, 10, 12, 0, 1, 86, 148, 158, 88, 70, 12, 14, 0, 1, 170, 336, 342, 288, 130, 96, 14, 16, 0, 1, 342, 716, 846, 648, 470, 180, 126, 16, 18, 0, 1

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..65.

Formula

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)}}

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

Example

Triangle begins
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, 54, 48, 10, 12, 0, 1

Crossrefs

Sequence in context: A131644 A115346 A140531 * A109189 A264157 A361853

Adjacent sequences: A117313 A117314 A117315 * A117317 A117318 A117319

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 07 2006

Status

approved