A147747 Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)).

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, 2239, 663, 135, 17, 1

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..54.

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

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[(1-3#+#^2)/(1-4#+3#^2)&, # (1-2#)/(1-4#+3#^2)&, 10] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

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