A147724 -id:A147724 - cp's OEIS frontend

A147725 Row sums of triangle in A147724.

1, 2, 10, 68, 502, 3770, 28408, 214202, 1615330, 12181748, 91867102, 692804690, 5224704088, 39401485202, 297141621850, 2240858259428, 16899166494502, 127443057596810, 961096686931768, 7247996548821002, 54659905383139570

Offset: 0

Philippe Deléham, Nov 15 2008

nonn

a(n)=9*a(n-1)-11*a(n-2) for n>2, a(0)=1, a(1)=2, a(2)=10. G.f.: (1-7x+3x^2)/(1-9x+11x^2).

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

Original entry on oeis.org

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

Paul Barry, Nov 11 2008

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

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

Cf. A147720.

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 *)

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

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

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A147725 Row sums of triangle in A147724.

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

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