A147723 Riordan array (1, x(1 - 4x)/(1 - 7x + 3x^2)).

1, 0, 1, 0, 3, 1, 0, 18, 6, 1, 0, 117, 45, 9, 1, 0, 765, 342, 81, 12, 1, 0, 5004, 2556, 702, 126, 15, 1, 0, 32733, 18810, 5859, 1224, 180, 18, 1, 0, 214119, 136719, 47493, 11241, 1935, 243, 21, 1

Offset: 0

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

Comments

[0,3,3,1,0,0,0,....] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938. A147723*A007318 is A147724.

Examples

			Triangle begins
  1;
  0,   1;
  0,   3,   1;
  0,  18,   6,   1;
  0, 117,  45,   9,   1;
  0, 765, 342,  81,  12,   1;
  ...
		

Crossrefs

Cf. A147720.

Programs

Mathematica

T[0,0] = T[1,1]= T[2,2] = 1; T[1,0] = T[2,0] = 0; T[2,1] = 3; T[n_, k_]:= If[k<0 || k>n, 0, 7 T[n - 1, k] + T[n - 1, k - 1] - 3 T[n - 2, k] - 4 T[n - 2, k - 1]]; Flatten[Table[ T[n, k], {n, 0, 8}, {k, 0, n}]] (* Indranil Ghosh, Mar 10 2017, after Philippe Deléham *)

PARI

T(n, k)= if(n==k, 1, if(k==0, 0, if(n==2 && k==1, 3, if(k<0 || k>n, 0, 7*T(n - 1, k) + T(n - 1, k - 1) - 3*T(n - 2, k) - 4*T(n - 2, k - 1)))));
{for(n=0, 8, for(k=0, n, print1(T(n,k),", ");); print();); } \\ Indranil Ghosh, Mar 10 2017

Formula

G.f.: (1 - 7*x + 4*x^2)/(1 - (7+y)*x + (3+4*y)*x^2). - Philippe Deléham, Jan 11 2012

T(n,k) = 7*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - 4*T(n-2,k-1), T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0, T(2,1) = 3, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Nov 02 2013