A124369 Riordan array (1/((1-x-x^2)(1+x+x^2)),x(1+x)/((1-x-x^2)(1+x+x^2))).

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, 48, 50, 34, 16, 6, 1, 17, 58, 103, 110, 91, 52, 22, 7, 1, 28, 104, 200, 250, 220, 152, 76, 29, 8, 1, 44, 188, 385, 534, 530, 400, 239, 107, 37, 9, 1

Offset

0,7

Comments

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

Links

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

Formula

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};

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

Example

Triangle begins
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, 48, 50, 34, 16, 6, 1,
17, 58, 103, 110, 91, 52, 22, 7, 1

Crossrefs

Sequence in context: A327799 A198199 A366039 * A205013 A138258 A359812

Adjacent sequences: A124366 A124367 A124368 * A124370 A124371 A124372

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 27 2006

Status

approved