A099094 -id:A099094 - cp's OEIS frontend

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, 177147, 59049

Offset: 0

Paul Barry, Sep 25 2004

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. - Philippe Deléham, Dec 18 2008

			Rows begin:
  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;
  ...

Cf. A038221.

[[Binomial(k,n-k)*3^k: k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Feb 21 2015 /* as the triangle */

tabl(nn) = {for (n=0, nn, for (k=0, n, print1(binomial(k, n-k)*3^k, ", ");); print(););} \\ Michel Marcus, Feb 21 2015

T(n,k) = binomial(k, n-k)*3^k. - corrected by Michel Marcus, Feb 21 2015
Columns have g.f. (3x+3x^3)^k.
T(n,k) = A026729(n,k)*3^k. - Philippe Deléham, Jul 29 2006

cp's OEIS Frontend

A099465 Duplicate of A099094.

Views

Author

Keywords

A099093 Riordan array (1, 3+3x).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

PARI

Formula