A147746 - OEIS

A147746

Riordan array (1, x(1-2x)/(1-3x+x^2)).

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 5, 3, 1, 0, 13, 14, 9, 4, 1, 0, 34, 40, 28, 14, 5, 1, 0, 89, 114, 87, 48, 20, 6, 1, 0, 233, 323, 267, 161, 75, 27, 7, 1, 0, 610, 910, 809, 528, 270, 110, 35, 8, 1

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OFFSET

0,8

COMMENTS

Triangle [0,1,1,1,0,0,0,....] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938.

Note that 1/(1-x/(1-x/(1-x))) = (1-2x)/(1-3x+x^2). Row sums are A124302.

A147746*A007318 = A147747.

LINKS

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

FORMULA

Sum_{k=0..n} T(n,k)*2^k = A147748(n). - Philippe Deléham, Oct 30 2011

Sum_{k=0..n} T(n,k)*(-1)^(n-k) = A215936(n). - Philippe Deléham, Aug 30 2012

G.f.: (1 - 3*x + x^2)/(1 - 3*x + x^2 - x*y + 2*x^2*y). - R. J. Mathar, Aug 11 2015

EXAMPLE

Triangle begins

0, 1;

0, 1, 1;

0, 2, 2, 1;

0, 5, 5, 3, 1;

0, 13, 14, 9, 4, 1;

0, 34, 40, 28, 14, 5, 1;

0, 89, 114, 87, 48, 20, 6, 1;

...

MATHEMATICA

(* The function RiordanArray is defined in A256893. *)

RiordanArray[1&, # (1-2#)/(1-3#+#^2)&, 10] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

CROSSREFS

Sequence in context: A112161 A128497 A011434 * A059365 A106566 A099039

Adjacent sequences: A147743 A147744 A147745 * A147747 A147748 A147749

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 11 2008

STATUS

approved