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Number triangle related to the Fibonacci polynomials.
3

%I #9 Mar 10 2019 01:43:15

%S 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,

%T 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,

%U 84,165,66,91,15,17,1,1,1,21,70,210,165,286,91,120,17,19,1,1,1,21,126,210

%N Number triangle related to the Fibonacci polynomials.

%C 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.

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

%F T(n,k) = A065941(n+k,n-k). - _Johannes W. Meijer_, Aug 14 2011

%e Rows begin

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 1, 1;

%e 1, 3, 5, 1, 1;

%e 1, 6, 5, 7, 1, 1;

%e 1, 6, 15, 7, 9, 1, 1;

%p 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

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Jun 22 2005