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

0,2

Links

Table of n, a(n) for n=0..35.

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

Example

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.

Sequence in context: A162406 A129282 A073153 * A362609 A238656 A077882

Adjacent sequences: A073151 A073152 A073153 * A073155 A073156 A073157

Keyword

easy,nonn,tabl

Author

Paul D. Hanna, Jul 29 2002

Status

approved