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A216238 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, 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 A216238 #16 Mar 19 2013 07:03:19
%S A216238 1,1,0,1,1,0,1,2,0,0,1,3,2,0,0,0,4,5,0,0,0,0,4,9,5,0,0,0,0,0,13,14,0,
%T A216238 0,0,0,0,0,13,27,14,0,0,0,0,0,0,0,40,41,0,0,0,0,0,0,0,0,40,81,41,0,0,
%U A216238 0,0,0,0,0,0,0,121,122,0,0,0,0,0,0
%N A216238 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, 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 A216238 Hexagon arithmetic of E. Lucas.
%D A216238 E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome1, p.89
%H A216238 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 A216238 T(n,n) = A124302(n).
%F A216238 T(n,n+1) = A124302(n+1).
%F A216238 T(n,n+2) = 3^n = A000244(n).
%F A216238 T(n,n+3) = T(n,n+4) = A003462(n+1).
%F A216238 Sum_{k, 0<=k<=n} T(n-k,k) = A182522(n).
%e A216238 Square array begins:
%e A216238 1, 1, 1, 1,  1,  0,   0,   0,   0,    0,    0, ... row n=0
%e A216238 0, 1, 2, 3,  4,  4,   0,   0,   0,    0,    0, ... row n=1
%e A216238 0, 0, 2, 5,  9, 13,  13,   0,   0,    0,    0, ... row n=2
%e A216238 0, 0, 0, 5, 14, 27,  40,  40,   0,    0,    0, ... row n=3
%e A216238 0, 0, 0, 0, 14, 41,  81, 121, 121,    0,    0, ... row n=4
%e A216238 0, 0, 0, 0,  0, 41, 122, 243, 364,  364,    0, ... row n=5
%e A216238 0, 0, 0, 0,  0,  0, 122, 365, 729, 1093, 1093, ... row n=6
%e A216238 ...
%Y A216238 Cf. A000244, A003462, A124302, A182522.
%Y A216238 Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236.
%K A216238 nonn,tabl
%O A216238 0,8
%A A216238 _Philippe Deléham_, Mar 14 2013