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%I #27 Nov 17 2018 12:00:04
%S 1,1,1,1,2,1,1,3,3,0,1,4,6,3,0,0,5,10,9,0,0,0,5,15,19,9,0,0,0,0,20,34,
%T 28,0,0,0,0,0,20,54,62,28,0,0,0,0,0,0,74,116,90,0,0,0,0,0,0,0,74,190,
%U 206,90,0,0,0,0,0,0,0,0,264,396,296,0,0,0,0,0,0,0,0,0,264,660,692,296,0,0,0,0,0
%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 3 or if k-n >= 5, T(2,0) = 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.
%D E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89.
%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) = A094817(n), for n > 0.
%F T(n+1,n) = T(n+2,n) = A094803(n).
%F T(n,n+1) = A007052(n).
%F T(n,n+2) = A094821(n+1).
%F T(n,n+3) = T(n,n+4) = A094806(n).
%F Sum_{k=0..n} T(n-k,k) = A217730(n). - _Philippe Deléham_, Mar 22 2013
%e Square array begins:
%e 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ... row n=0
%e 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ... row n=1
%e 1, 3, 6, 10, 15, 20, 20, 0, 0, 0, 0, ... row n=2
%e 0, 3, 9, 19, 34, 54, 74, 74, 0, 0, 0, ... row n=3
%e 0, 0, 9, 28, 62, 116, 190, 264, 264, 0, 0, ... row n=4
%e 0, 0, 0, 28, 90, 206, 396, 660, 924, 924, 0, ... row n=5
%e ...
%e Array, read by rows, with 0 omitted:
%e 1, 1, 1, 1, 1
%e 1, 2, 3, 4, 5, 5
%e 1, 3, 6, 10, 15, 20, 20
%e 3, 9, 19, 34, 54, 74, 74
%e 9, 28, 62, 116, 190, 264, 264
%e 28, 90, 206, 396, 660, 924, 924
%e 90, 296, 692, 1352, 2276, 3200, 3200
%e ...
%Y Cf. A007052, A094803, A094806, A094817, A094821
%Y Cf. similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230.
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Mar 14 2013
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