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

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• nonn
• tabl

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.

Examples

			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
		

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)}