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Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.
1

%I #4 Feb 03 2015 20:20:16

%S 1,1,1,1,1,1,1,2,2,1,1,3,5,3,1,1,5,13,13,5,1,1,8,34,55,34,8,1,1,13,89,

%T 233,233,89,13,1,1,21,233,987,1597,987,233,21,1,1,34,610,4181,10946,

%U 10946,4181,610,34,1,1,55,1597,17711,75025,121393,75025,17711,1597,55,1

%N Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 2, 2, 1;

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

%e 1, 5, 13, 13, 5, 1;

%e 1, 8, 34, 55, 34, 8, 1;

%e 1, 13, 89, 233, 233, 89, 13, 1;

%e 1, 21, 233, 987, 1597, 987, 233, 21, 1;

%e 1, 34, 610, 4181, 10946, 10946, 4181, 610, 34, 1;

%e 1, 55, 1597, 17711, 75025, 121393, 75025, 17711, 1597, 55, 1; ...

%t Flatten[Table[Fibonacci[k(n-k)+1],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Feb 03 2015 *)

%o (PARI) T(n,k)=fibonacci(k*(n-k)+1)

%Y Cf. A135967.

%K nonn,tabl

%O 0,8

%A _Paul D. Hanna_, Dec 11 2007