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A147747 Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)). 4
1, 1, 1, 2, 3, 1, 5, 9, 5, 1, 14, 28, 20, 7, 1, 41, 89, 75, 35, 9, 1, 122, 285, 273, 154, 54, 11, 1, 365, 913, 974, 634, 273, 77, 13, 1, 1094, 2918, 3420, 2502, 1256, 440, 104, 15, 1, 3281, 9297, 11850, 9578, 5439 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

Row sums are A147748. A147747=A147746*A007318.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - 2*T(n-2,k-1), T(0,0) = T(0,1) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3, T(n,k) = 0 if k>n or if k<0. - Philippe Deléham, Oct 29 2013

G.f.: (1 - 3*x + x^2)/(1 - 4*x + 3*x^2 - x*y + 2*x^2*y). - Philippe Deléham, Oct 29 2013

EXAMPLE

Triangle begins

1,

1, 1,

2, 3, 1,

5, 9, 5, 1,

14, 28, 20, 7, 1,

41, 89, 75, 35, 9, 1,

122, 285, 273, 154, 54, 11, 1

CROSSREFS

Sequence in context: A236843 A055905 A147703 * A039599 A154380 A155083

Adjacent sequences:  A147744 A147745 A147746 * A147748 A147749 A147750

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 11 2008

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)