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

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

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.

Examples

			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
		

Programs

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 *)

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