A054126 Odd-index Fibonacci row-sum array: T(n,k)=U(2n+1,n+1+k), 0<=k<=n, n >= 0, U the array in A054125.

2, 3, 2, 6, 5, 2, 12, 13, 7, 2, 24, 30, 24, 9, 2, 48, 65, 68, 39, 11, 2, 96, 136, 171, 134, 58, 13, 2, 192, 279, 398, 394, 236, 81, 15, 2, 384, 566, 880, 1040, 802, 382, 108, 17, 2, 768, 1141, 1880, 2542, 2396, 1479, 580, 139, 19, 2, 1536

Offset

0,1

Links

Table of n, a(n) for n=0..55.

Formula

From Jianing Song, May 30 2022: (Start)

T(n,k) = 2 if k = n, otherwise A052509(2n,n+1+k) + A052509(2n,n-k) = 2^(n-1-k) + Sum_{m=0..n-k} binomial(n+k,m) = 2^(n-1-k) + 2^(n+k) - Sum_{m=0..2*k-1} binomial(n+k,m).

T(n,k) = [x^n*y^(n-k)] (1-x*y) * ((1+y-x*y^2)/((1-x*y^2)*((1-x*y)^2-x)) + (1+y-x*y)/((1-x)*((1-x*y)^2-x*y^2))). (End)

Example

Rows:
   2;
   3,  2;
   6,  5, 2;
  12, 13, 7, 2;
  ...

Prog

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

Crossrefs

Sequence in context: A286586 A113710 A286587 * A323507 A144176 A307686

Adjacent sequences: A054123 A054124 A054125 * A054127 A054128 A054129

Keyword

nonn,tabl,eigen

Author

Clark Kimberling

Status

approved