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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, 177147, 59049 (list; table; graph; refs; listen; history; text; 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. - Philippe Deléham, Dec 18 2008

LINKS

Table of n, a(n) for n=0..65.

FORMULA

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

EXAMPLE

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;

...

PROG

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

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

CROSSREFS

Cf. A038221.

Sequence in context: A010030 A197270 A117940 * A137339 A230184 A132330

Adjacent sequences:  A099090 A099091 A099092 * A099094 A099095 A099096

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 25 2004

STATUS

approved

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Last modified February 25 03:33 EST 2018. Contains 299630 sequences. (Running on oeis4.)