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

0,1

Comments

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

Links

Table of n, a(n) for n=0..73.

Formula

From Jianing Song, May 30 2022:

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)

Example

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

Prog

(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

Crossrefs

Sequence in context: A029243 A306240 A109829 * A177227 A174373 A232270

Adjacent sequences: A054122 A054123 A054124 * A054126 A054127 A054128

Keyword

nonn,tabl,eigen

Author

Clark Kimberling

Status

approved