A073154 Triangle of numbers relating two sequences (A073157 and A073155).

1, 2, 4, 5, 9, 14, 18, 28, 38, 56, 70, 106, 131, 167, 237, 293, 433, 523, 613, 753, 1046, 1283, 1869, 2219, 2543, 2893, 3479, 4762, 5808, 8374, 9839, 11099, 12359, 13824, 16390, 22198

Offset: 0

Author

Paul D. Hanna, Jul 29 2002

Keywords

• easy
• nonn
• tabl

Examples

			a(4,0)=a(3,3)+a(2,2)=56+14=70.
a(5,2)=A073157(0)*A073157(5)+A073157(1)*A073157(4)+A073157(2)*A073157(3)= 1*293+2*70+5*18=523.
Rows:
  {1};
  {2,4};
  {5,9,14};
  {18,28,38,56};
  {70,106,131,167,237};
  {293,433,523,613,753,1046};
  {1283,1869,2219,2543,2893,3479,4762};
  ...
		

Crossrefs

Cf. A073153, A073155, A073156, A073157, A073152.

Formula

Triangle {a(n, k), n >= 0, 0<=k<=n} defined by: a(0, 0)=1, a(n, 0)=A073157(n), a(n, n)=A073155(n+1), a(n, 0)=a(n-1, n-1) + a(n-2, n-2), a(n, k)=sum{j=0..k} A073157(j) * A073157(n-j).

G.f.: Sum_{n>=0, 0<=k<=n} a(n, k) x^n y^k = A(x*y)(A(x) - y A(x*y))/(1 - y) where A(x) = (1 - (1 - 4 x (1 + x)^2)^(1/2))/(2 x (1 + x)) is the o.g.f. for A073157. - David Callan, Aug 16 2006