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A099092 Riordan array (1,2+4x). 0
1, 0, 2, 0, 4, 4, 0, 0, 16, 8, 0, 0, 16, 48, 16, 0, 0, 0, 96, 128, 32, 0, 0, 0, 64, 384, 320, 64, 0, 0, 0, 0, 512, 1280, 768, 128, 0, 0, 0, 0, 256, 2560, 3840, 1792, 256, 0, 0, 0, 0, 0, 2560, 10240, 10752, 4096, 512, 0, 0, 0, 0, 0, 1024, 15360, 35840, 28672, 9216, 1024, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are A063727. Diagonal sums are A052907.

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..68.

FORMULA

Number triangle T(n,k) = binomial(k, n-k)*2^n; columns have g.f. (2x+4x^2)^k.

T(n,k) = A113953(n,k)*2^k = A026729(n,k)*2^n. - Philippe Deléham, Dec 11 2008

EXAMPLE

Rows begin

  {1},

  {0,  2},

  {0,  4,  4},

  {0,  0, 16,  8},

  {0,  0, 16, 48, 16}, ...

CROSSREFS

Cf. A026729, A038210, A052907, A063727, A113953.

Sequence in context: A277333 A248663 A093443 * A177806 A286550 A307658

Adjacent sequences:  A099089 A099090 A099091 * A099093 A099094 A099095

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 25 2004

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)