login
Sum of the arrays in A054123 and A054124.
2

%I #19 May 30 2022 08:24:16

%S 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,

%T 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,

%U 39,32,39,46,31,10,2,2,11,39,68,65,48,48,65

%N Sum of the arrays in A054123 and A054124.

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

%F From _Jianing Song_, May 30 2022:

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

%F 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)

%e Rows:

%e 2;

%e 2,2;

%e 2,2,2;

%e 2,3,3,2;

%e ...

%o (PARI) A052509(n,k) = sum(m=0, k, binomial(n-k, m));

%o T(n,k) = if(k==0 || k==n, 2, A052509(n-1,k) + A052509(n-1,n-k)) \\ _Jianing Song_, May 30 2022

%K nonn,tabl,eigen

%O 0,1

%A _Clark Kimberling_