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%I #16 Apr 05 2013 12:27:01
%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,0,1,5,10,10,4,0,0,6,15,20,14,0,0,0,6,21,
%T 35,34,14,0,0,0,0,27,56,69,48,0,0,0,0,0,27,83,125,117,48,0,0,0,0,0,0,
%U 110,208,242,165,0,0,0,0,0,0,0,110,318,450,407,165
%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=4 or if k-n >= 6, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C A hexagon arithmetic of E. Lucas.
%F T(n,n+4) = T(n,n+5) = A094788(n+2).
%F T(n,n+3) = A217783(n).
%F T(n,n+2) = A217779(n).
%F T(n,n+1) = A081567(n).
%F T(n,n) = A217782(n).
%F T(n+1,n) = A217778(n).
%F T(n+3,n) = T(n+2,n) = A094667(n+1).
%F Sum(T(n-k,k), k=0..n) = A217777(n).
%e Square array begins:
%e n=0: 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
%e n=1: 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, ...
%e n=2: 1, 3, 6, 10, 15, 21, 27, 27, 0, 0, 0, 0, ...
%e n=3: 1, 4, 10, 20, 35, 56, 83, 110, 110, 0, 0, 0, ...
%e n=4: 0, 4, 14, 34, 69, 125, 208, 318, 428, 428, 0, 0, ...
%e n=5: 0, 0, 14, 48, 117, 242, 450, 768, 1196, 1624, 1624, 0, ...
%e ...
%e Square array, read by rows, with 0 omitted:
%e ...1, 1, 1, 1, 1, 1
%e ...1, 2, 3, 4, 5, 6, 6
%e ...1, 3, 6, 10, 15, 21, 27, 27
%e ...1, 4, 10, 20, 35, 56, 83, 110, 110
%e ...4, 14, 34, 69, 125, 208, 318, 428, 428
%e ..14, 48, 117, 242, 450, 768, 1196, 1624, 1624
%e ..48, 165, 407, 857, 1625, 2821, 4445, 6069, 6069
%e .165, 572, 1429, 3054, 5875, 10320, 16389, 22458, 22458
%e .572, 2001, 5055, 10930, 21250, 37639, 60097, 82555, 82555
%e 2001, 7056, 17986, 39236, 76875, 136972, 219527, 302082, 302082
%e ...
%e Triangle begins:
%e 1
%e 1, 1
%e 1, 2, 1
%e 1, 3, 3, 1
%e 1, 4, 6, 4, 0
%e 1, 5, 10, 10, 4, 0
%e 0, 6, 15, 20, 14, 0, 0
%e 0, 6, 21, 35, 34, 14, 0, 0
%e ...
%Y Cf. Similar sequences: A214846, A216054, A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236, A216238, A217257, A217315, A217593, A217765.
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Mar 24 2013