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%I #23 Aug 01 2017 11:47:51
%S 1,1,2,2,3,5,3,5,8,13,5,8,13,21,34,8,13,21,34,55,89,13,21,34,55,89,
%T 144,233,21,34,55,89,144,233,377,610,34,55,89,144,233,377,610,987,
%U 1597,55,89,144,233,377,610,987,1597,2584,4181
%N Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).
%H Michel Marcus, <a href="/A199512/b199512.txt">Rows n=0..50 of triangle, flattened</a>
%H László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Nemeth/nemeth2.html">On the Binomial Interpolated Triangles</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.7.8. See p. 15.
%F T(n,k) = T(n,k-1) + T(n-1,k-1) = T(n-1,k-1) + T(n-1,k).
%F T(n,0) = Fibonacci(n+1) = A000045(n+1).
%e Triangle begins :
%e 1
%e 1, 2
%e 2, 3, 5
%e 3, 5, 8, 13
%e 5, 8, 13, 21, 34
%e 8, 13, 21, 34, 55, 89
%o (PARI) T(n, k) = fibonacci(n+k+1);
%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Aug 01 2017
%Y Cf. A000045, A199334.
%Y Rows sums : A096140, Diagonal sums : A128620.
%K easy,nonn,tabl
%O 0,3
%A _Philippe Deléham_, Nov 07 2011
%E More terms from _Michel Marcus_, Aug 01 2017
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