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A217257 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%I A217257 #20 Oct 20 2021 12:37:42
%S A217257 1,1,0,1,1,0,1,2,0,0,1,3,2,0,0,1,4,5,0,0,0,1,5,9,5,0,0,0,0,6,14,14,0,
%T A217257 0,0,0,0,6,20,28,14,0,0,0,0,0,0,26,48,42,0,0,0,0,0,0,0,26,74,90,42,0,
%U A217257 0,0,0,0,0,0,0,100,164,132,0,0,0,0,0,0,0,0,0,100,264,296,132,0,0,0,0,0,0,0,0,0,0,364,560,428,0,0,0,0,0,0,0,0,0
%N A217257 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C A217257 A hexagon arithmetic of E. Lucas.
%D A217257 E. Lucas, Théorie des nombres, A. Blanchard, Paris, 1958, p.89
%H A217257 E. Lucas, <a href="http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-29021&amp;M=tdm">Théorie des nombres</a>, Tome 1, Jacques Gabay, Paris, p. 89
%F A217257 T(n,n) = A024175(n).
%F A217257 T(n,n+1) = A024175(n+1).
%F A217257 T(n,n+2) = A094803(n+1).
%F A217257 T(n,n+3) = A007070(n).
%F A217257 T(n,n+4) = A094806(n+2).
%F A217257 T(n,n+5) = T(n,n+6) = A094811(n+2).
%F A217257 Sum_{k, 0<=k<=n} T(n-k,k) = A030436(n).
%e A217257 Square array begins:
%e A217257 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0
%e A217257 0, 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1
%e A217257 0, 0, 2, 5, 9, 14, 20, 26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=2
%e A217257 0, 0, 0, 5, 14, 28, 48, 74, 100, 100, 0, 0, 0, 0, 0, 0, 0, ... row n=3
%e A217257 0, 0, 0, 0, 14, 42, 90, 162, 264, 364, 364, 0, 0, 0, 0, 0, ... row n=4
%e A217257 0, 0, 0, 0, 0, 42, 132, 296, 560, 924, 1288, 1288, 0, 0, 0, ... row n=5
%e A217257 ...
%Y A217257 Cf. similar sequences: A216230, A216228, A216226, A216238, A216054.
%K A217257 nonn,tabl
%O A217257 0,8
%A A217257 _Philippe Deléham_, Mar 17 2013
%E A217257 a(69) = 0 deleted by _Georg Fischer_, Oct 16 2021