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Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).
1

%I #16 Sep 06 2023 06:57:53

%S 1,1,1,2,2,1,3,4,3,1,5,8,7,4,1,8,15,16,11,5,1,13,28,34,28,16,6,1,21,

%T 51,70,66,45,22,7,1,34,92,140,148,116,68,29,8,1,55,164,274,320,281,

%U 190,98,37,9,1,89,290,527,672,651,494,295,136,46,10,1,144,509,999,1379,1456,1219,819,439,183,56,11,1

%N Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).

%C A Fibonacci related number triangle.

%H Seiichi Manyama, <a href="/A091594/b091594.txt">Rows n = 0..139, flattened</a>

%F k-th column has g.f. 1/(1-x-x^2) * ( x*(1-x^2)/(1-x-x^2) )^k.

%e Rows begin:

%e 1,

%e 1, 1,

%e 2, 2, 1,

%e 3, 4, 3, 1,

%e 5, 8, 7, 4, 1,

%e 8, 15, 16, 11, 5, 1,

%e 13, 28, 34, 28, 16, 6, 1,

%e 21, 51, 70, 66, 45, 22, 7, 1,

%e ...

%Y Columns include A000045, A029907, A054455. Row sums are A006054.

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Jan 23 2004