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%I #22 Nov 18 2018 09:55:09
%S 1,1,1,1,2,0,1,3,2,0,1,4,5,0,0,0,5,9,5,0,0,0,5,14,14,0,0,0,0,0,19,28,
%T 14,0,0,0,0,0,19,47,42,0,0,0,0,0,0,0,66,89,42,0,0,0,0,0,0,0,66,155,
%U 131,0,0,0,0,0,0,0,0,0,221,286,131,0,0,0,0,0,0,0,0,0,221,507,417,0,0,0,0,0,0
%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 2 or if k-n >= 5, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C Arithmetic hexagon of E. Lucas.
%H E. Lucas, <a href="https://archive.org/details/thoriedesnombre00lucagoog/page/n119">Théorie des nombres</a>, Gauthier-Villars, Paris 1891, Tome 1, p. 89.
%F T(n,n) = T(n+1,n) = A080937(n+1).
%F T(n,n+1) = A094790(n+1).
%F T(n,n+2) = A094789(n+1).
%F T(n,n+3) = T(n,n+4) = A005021(n).
%F Sum_{k=0..n} T(n-k,k) = A028495(n+1). - _Philippe Deléham_, Mar 23 2013
%e Square array begins:
%e 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, ... row n=0
%e 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, ... row n=1
%e 0, 2, 5, 9, 14, 19, 19, 0, 0, 0, ... row n=2
%e 0, 0, 5, 14, 28, 47, 66, 66, 0, 0, ... row n=3
%e 0, 0, 0, 14, 42, 89, 155, 221, 221, 0, ... row n=4
%e 0, 0, 0, 0, 42, 131, 286, 507, 728, 728, ... row n=5
%e ...
%Y Cf. A005021, A080937, A094789, A094790.
%Y Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232.
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Mar 14 2013
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