|
| |
|
|
A099093
|
|
Riordan array (1,3+3x).
|
|
2
| |
|
|
1, 0, 3, 0, 3, 9, 0, 0, 18, 27, 0, 0, 9, 81, 81, 0, 0, 0, 81, 324, 243, 0, 0, 0, 27, 486, 1215, 729, 0, 0, 0, 0, 324, 2430, 4374, 2187, 0, 0, 0, 0, 81, 2430, 10935, 15309, 6561, 0, 0, 0, 0, 0, 1215, 14580, 45927, 52488, 19683, 0, 0, 0, 0, 0, 243, 10935, 76545, 183708
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Row sums are A030195. Diagonal sums are A099094. 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).
Modulo 2, this sequence gives A106344 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2008]
|
|
|
FORMULA
| Number triangle T(n, k)=binomial(k, n-k)3^n; Columns have g.f. (3x+3x^3)^k.
T(n,k)=A026729(n,k)*3^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 29 2006
|
|
|
EXAMPLE
| Rows begin {1}, {0,3}, {0,3,9}, {0,0,18,27}, {0,0,9,81,81},...
|
|
|
CROSSREFS
| Cf. A038221.
Sequence in context: A010030 A197270 A117940 * A137339 A132330 A117078
Adjacent sequences: A099090 A099091 A099092 * A099094 A099095 A099096
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 25 2004
|
| |
|
|
