A054125 Sum of the arrays in A054123 and A054124.

2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 4, 4, 4, 2, 2, 5, 6, 6, 5, 2, 2, 6, 9, 8, 9, 6, 2, 2, 7, 13, 12, 12, 13, 7, 2, 2, 8, 18, 19, 16, 19, 18, 8, 2, 2, 9, 24, 30, 24, 24, 30, 24, 9, 2, 2, 10, 31, 46, 39, 32, 39, 46, 31, 10, 2, 2, 11, 39, 68, 65, 48, 48, 65

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl
• eigen

Comments

Row sums are twice Fibonacci numbers, A006355(n+2).

Examples

			Rows:
  2;
  2,2;
  2,2,2;
  2,3,3,2;
  ...
		

Programs

PARI

A052509(n,k) = sum(m=0, k, binomial(n-k, m));
T(n,k) = if(k==0 || k==n, 2, A052509(n-1,k) + A052509(n-1,n-k)) \\ Jianing Song, May 30 2022

Formula

From Jianing Song, May 30 2022: (Start)

T(n,k) = 2 if k = 0 or k = n, A052509(n-1,k) + A052509(n-1,n-k) otherwise.

G.f.: Sum_{n>=0, 0<=k<=n} T(n,k) * x^n * y^k = (1-x^2*y) * (1/((1-x*y)*(1-x-x^2*y)) + 1/((1-x)*(1-x*y-x^2*y))). (End)