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A216201 Square array T, read by antidiagonals : T(n,k) = 0 if n-k>=3 or if k-n>=4, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%I A216201 #10 Mar 16 2013 10:26:43
%S A216201 1,1,1,1,2,1,1,3,3,0,0,4,6,3,0,0,4,10,9,0,0,0,0,14,19,9,0,0,0,0,14,33,
%T A216201 28,0,0,0,0,0,0,47,61,28,0,0,0,0,0,0,47,108,89,0,0,0,0,0,0,0,0,155,
%U A216201 197,89,0,0,0,0
%N A216201 Square array T, read by antidiagonals : T(n,k) = 0 if n-k>=3 or if k-n>=4, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%D A216201 E. Lucas, Théorie des nombres, Tome 1, Albert Blanchard, Paris, 1958, p.89
%H A216201 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 A216201 T(n,n) = A052975(n).
%F A216201 T(n,n+1) = A060557(n).
%F A216201 T(n+1,n) = T(n+2,n) = A094790(n+1).
%F A216201 T(n,n+2) = T(n,n+3) = A094789(n+1).
%F A216201 Sum_{k, 0<=k<=n} T(n-k,k) = (-1)^n*A078038(n).
%e A216201 Square array begins:
%e A216201 1, 1, 1,  1,  0,   0,   0,   0,   0,   0, 0, 0, 0, ... row n = 0
%e A216201 1, 2, 3,  4,  4,   0,   0,   0,   0,   0, 0, 0, 0, ... row n = 1
%e A216201 1, 3, 6, 10, 14,  14,   0,   0,   0,   0, 0, 0, 0, ... row n = 2
%e A216201 0, 3, 9, 19, 33,  47,  47,   0,   0,   0, 0, 0, 0, ... row n = 3
%e A216201 0, 0, 9, 28, 61, 108, 155, 155,   0,   0, 0, 0, 0, ... row n = 4
%e A216201 0, 0, 0, 28, 89, 197, 352, 507, 507,   0, 0, 0, 0, ... row n = 5
%e A216201 0, 0, 0,  0, 89, 286, 638,1147,1652,1652, 0, 0, 0, ... row n = 6
%e A216201 ...
%Y A216201 Cf. A052975, A060557, A078038, A095789, A094790
%K A216201 nonn,tabl
%O A216201 0,5
%A A216201 _Philippe Deléham_, Mar 12 2013