A099095 Riordan array (1,3+2x).

1, 0, 3, 0, 2, 9, 0, 0, 12, 27, 0, 0, 4, 54, 81, 0, 0, 0, 36, 216, 243, 0, 0, 0, 8, 216, 810, 729, 0, 0, 0, 0, 96, 1080, 2916, 2187, 0, 0, 0, 0, 16, 720, 4860, 10206, 6561, 0, 0, 0, 0, 0, 240, 4320, 20412, 34992, 19683, 0, 0, 0, 0, 0, 32, 2160, 22680, 81648, 118098, 59049, 0, 0

Offset

0,3

Comments

Row sums are A007482. Diagonal sums are A053088. 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..67.

Eric W. Weisstein, Fermat Polynomial

Formula

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

Example

Rows begin {1}, {0,3}, {0,2,9}, {0,0,12,27}, {0,0,4,54,81},...

Crossrefs

Cf. A038220.

Sequence in context: A330646 A341905 A354905 * A061980 A059683 A030208

Adjacent sequences: A099092 A099093 A099094 * A099096 A099097 A099098

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 25 2004

Status

approved