A099091 Riordan array (1,2+3x).

1, 0, 2, 0, 3, 4, 0, 0, 12, 8, 0, 0, 9, 36, 16, 0, 0, 0, 54, 96, 32, 0, 0, 0, 27, 216, 240, 64, 0, 0, 0, 0, 216, 720, 576, 128, 0, 0, 0, 0, 81, 1080, 2160, 1344, 256, 0, 0, 0, 0, 0, 810, 4320, 6048, 3072, 512, 0, 0, 0, 0, 0, 243, 4860, 15120, 16128, 6912, 1024, 0, 0, 0, 0, 0, 0

Offset

0,3

Comments

Row sums are A015518(n+1). Diagonal sums are A002447. The Riordan array (1,s+tx) defines T(n,k)=binomial(k,n-k)s^k(t/s)^(n-k). The row sums satisfy a(n)=s*a(n-1)+t*a(n-2) and the diagonal sums satisfy a(n)=s*a(n-2)+t*a(n-3).

Links

Table of n, a(n) for n=0..71.

Formula

Number triangle T(n, k)=binomial(k, n-k)2^k*(3/2)^(n-k) Columns have g.f. (2x+3x^2)^k.

Example

Rows begin
1;
0,2;
0,3,4;
0,0,12,8;
0,0,9,36,16;

Crossrefs

Sequence in context: A224226 A153250 A102389 * A227595 A078436 A368090

Adjacent sequences: A099088 A099089 A099090 * A099092 A099093 A099094

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 25 2004

Status

approved