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Triangle read by rows: columns are Fibonacci numbers F_{2i+1} shifted downwards.
1

%I #15 Jul 14 2020 10:28:41

%S 1,2,1,5,2,1,13,5,2,1,34,13,5,2,1,89,34,13,5,2,1,233,89,34,13,5,2,1,

%T 610,233,89,34,13,5,2,1,1597,610,233,89,34,13,5,2,1,4181,1597,610,233,

%U 89,34,13,5,2,1,10946,4181,1597,610,233,89,34,13,5,2,1

%N Triangle read by rows: columns are Fibonacci numbers F_{2i+1} shifted downwards.

%C A Riordan array.

%H Rémy Sigrist, <a href="/A328082/b328082.txt">Table of n, a(n) for n = 1..5050</a>

%H Rigoberto Flórez, Leandro Junes, José L. Ramírez, <a href="https://doi.org/10.1016/j.disc.2019.06.018">Enumerating several aspects of non-decreasing Dyck paths</a>, Discrete Mathematics (2019) Vol. 342, Issue 11, 3079-3097. See page 3083.

%e Triangle begins:

%e 1;

%e 2, 1;

%e 5, 2, 1;

%e 13, 5, 2, 1;

%e 34, 13, 5, 2, 1;

%e 89, 34, 13, 5, 2, 1;

%e 233, 89, 34, 13, 5, 2, 1;

%e 610, 233, 89, 34, 13, 5, 2, 1;

%e 1597, 610, 233, 89, 34, 13, 5, 2, 1;

%e ...

%o (PARI) T(n,k) = fibonacci(2*(n-k)+1) \\ _Rémy Sigrist_, Jul 14 2020

%Y Cf. A000045.

%K nonn,tabl

%O 1,2

%A _N. J. A. Sloane_, Oct 15 2019

%E More terms from _Rémy Sigrist_, Jul 14 2020