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A122016 Riordan array(1,x*(1+2*x)/(1-x)). 3
1, 0, 1, 0, 3, 1, 0, 3, 6, 1, 0, 3, 15, 9, 1, 0, 3, 24, 36, 12, 1, 0, 3, 33, 90, 66, 15, 1, 0, 3, 42, 171, 228, 105, 18, 1, 0, 3, 51, 279, 579, 465, 153, 21, 1, 0, 3, 60, 414, 1200, 1500, 828, 210, 24, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Triangle T(n,k), 0<=k<=n, read by rows given by [0,3,-2,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . Rising and falling diagonals are A078010 and A122552.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A026150(n), A102900(n) for x = 1, 2.

T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k-1) . - Philippe Deléham, Sep 25 2006

G.f.: (1-x)/(1-(y+1)*x-2*y*x^2). - Philippe Deléham, Jan 31 2012

Sum_{k, 0<=k<=n} T(n,k)*x^k = A117575(n+1), A000007(n), A026150(n), A122117(n), A147518(n) for x = -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Jan 31 2012

EXAMPLE

Triangle begins:

1;

0, 1;

0, 3, 1;

0, 3, 6, 1;

0, 3, 15, 9, 1;

0, 3, 24, 36, 12, 1;

0, 3, 33, 90, 66, 15, 1;

0, 3, 42, 171, 228, 105, 18, 1;

0, 3, 51, 279, 579, 465, 153, 21, 1;

0, 3, 60, 414, 1200, 1500, 828, 210, 24, 1;

CROSSREFS

Cf. Diagonals A000012, A008585, A062741, columns A000007, A122553, A122709, row sums A026150.

Sequence in context: A049403 A104556 A116089 * A067882 A215771 A110033

Adjacent sequences:  A122013 A122014 A122015 * A122017 A122018 A122019

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Sep 24 2006

STATUS

approved

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Last modified May 23 11:05 EDT 2019. Contains 323513 sequences. (Running on oeis4.)