A117375 Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108.

1, 3, 1, 12, 4, 1, 51, 17, 5, 1, 222, 74, 23, 6, 1, 978, 326, 104, 30, 7, 1, 4338, 1446, 468, 142, 38, 8, 1, 19323, 6441, 2103, 657, 189, 47, 9, 1, 86310, 28770, 9447, 3006, 903, 246, 57, 10, 1, 386250, 128750, 42440, 13670, 4223, 1217, 314, 68, 11, 1, 1730832

Offset

0,2

Comments

Triangle factors as (1,xc(x))*(1/(1-3x),x). First row is A007854. Second row is A049027(n)-0^n. Row sums are A049027(n+1). Diagonal sums are A117376.

Links

Table of n, a(n) for n=0..55.

Formula

Number triangle T(0,0)=1, T(n,k)=[k<=n]*sum{j=0..n, (j/(n-j))*C(2n-j,n-j)[k<=j]*3^(j-k)}

Example

Triangle begins
1,
3, 1,
12, 4, 1,
51, 17, 5, 1,
222, 74, 23, 6, 1,
978, 326, 104, 30, 7, 1,
4338, 1446, 468, 142, 38, 8, 1
Production array begins
3, 1
3, 1, 1
3, 1, 1, 1
3, 1, 1, 1, 1
3, 1, 1, 1, 1, 1
3, 1, 1, 1, 1, 1, 1
3, 1, 1, 1, 1, 1, 1, 1
3, 1, 1, 1, 1, 1, 1, 1, 1
... - Philippe Deléham, Mar 05 2013

Crossrefs

Sequence in context: A287462 A287985 A337472 * A162995 A177020 A226167

Adjacent sequences: A117372 A117373 A117374 * A117376 A117377 A117378

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 10 2006

Status

approved