A109223 Number triangle related to the Fibonacci polynomials.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 6, 5, 7, 1, 1, 1, 6, 15, 7, 9, 1, 1, 1, 10, 15, 28, 9, 11, 1, 1, 1, 10, 35, 28, 45, 11, 13, 1, 1, 1, 15, 35, 84, 45, 66, 13, 15, 1, 1, 1, 15, 70, 84, 165, 66, 91, 15, 17, 1, 1, 1, 21, 70, 210, 165, 286, 91, 120, 17, 19, 1, 1, 1, 21, 126, 210

Offset

0,8

Comments

Riordan array (1/(1-x), x/(1-x^2)^2). Row-reversal of number triangle A109221. Diagonals form a repeated version of A054142. Row sums are A109222. Diagonal sums are A094967.

Links

Table of n, a(n) for n=0..81.

Formula

T(n,k) = binomial(floor((n+k)/2)+k, 2*k)

T(n,k) = A065941(n+k,n-k). - Johannes W. Meijer, Aug 14 2011

Example

Rows begin
  1;
  1,  1;
  1,  1,  1;
  1,  3,  1,  1;
  1,  3,  5,  1,  1;
  1,  6,  5,  7,  1,  1;
  1,  6, 15,  7,  9,  1,  1;

Maple

A109223 := proc(n, k): binomial(floor((n+k)/2)+k, 2*k) end: seq(seq(A109223(n, k), k=0..n), n=0..11); # Johannes W. Meijer, Aug 14 2011

Crossrefs

Sequence in context: A016733 A060234 A131270 * A263009 A283983 A016466

Adjacent sequences: A109220 A109221 A109222 * A109224 A109225 A109226

Keyword

easy,nonn,tabl

Author

Paul Barry, Jun 22 2005

Status

approved