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A216236 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=5, T(3,0) = 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).

%I A216236 #18 Mar 25 2013 04:30:17
%S A216236 1,1,1,1,2,1,1,3,3,1,1,4,6,4,0,0,5,10,10,4,0,0,5,15,20,14,0,0,0,0,20,
%T A216236 35,34,14,0,0,0,0,20,55,69,48,0,0,0,0,0,0,75,124,117,48,0,0,0,0,0,0,
%U A216236 75,199,241,165,0,0,0,0,0,0,0,0,274,440,406,165,0,0,0,0,0,0,0,0,274,714,846,571,0,0,0,0,0
%N A216236 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=5, T(3,0) = 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 A216236 Arithmetic hexagon of E. Lucas.
%D A216236 E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89
%H A216236 E. Lucas, <a href="http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&amp;O=NUMM-29021">Théorie des nombres</a>, Tome 1, Jacques Gabay, Paris, 1991, p.89
%F A216236 T(n+3,n) = T(n+2,n) = A094827(n).
%F A216236 T(n+1,n) = A094832(n).
%F A216236 T(n,n) = A094854(n).
%F A216236 T(n,n+1) = A094855(n).
%F A216236 T(n,n+2) = A094833(n+1).
%F A216236 T(n,n+3) = T(n,n+4) = A094828(n).
%F A216236 Sum( T(n-k,k), 0<=k<=n ) = A217733(n). - _Philippe Deléham_, Mar 22 2013
%e A216236 Square array begins:
%e A216236 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
%e A216236 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ...
%e A216236 1, 3, 6, 10, 15, 20, 20, 0, 0, 0, ...
%e A216236 1, 4, 10, 20, 35, 55, 75, 75, 0, 0, 0, ...
%e A216236 0, 4, 14, 34, 69, 124, 199, 274, 274, 0, 0, ...
%e A216236 0, 0, 14, 48, 117, 241, 440, 714, 988, 988, 0, ...
%e A216236 ...
%Y A216236 Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235.
%K A216236 nonn,tabl
%O A216236 0,5
%A A216236 _Philippe Deléham_, Mar 14 2013