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%I #7 Apr 14 2013 02:41:33
%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,0,0,6,15,20,15,5,0,0,6,21,
%T 35,35,20,0,0,0,0,27,56,70,55,20,0,0,0,0,27,83,126,125,75,0,0,0,0,0,0,
%U 110,209,251,200,75,0,0,0,0,0,0,110,319,460,451,275,0,0,0,0,0,0,0
%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 5 or if k-n >= 6, T(4,0) = 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).
%F sum(T(n-k,k), 0<=k<=n) = A223940(n).
%F T(n,n+5) = T(n,n+4) = A221863(n).
%F T(n,n+3) = A221862(n).
%F T(n,n+2) = A221859(n).
%F T(n,n+1) = A216710(n).
%F T(n,n) = A224514(n).
%F T(n+1,n) = A224509(n).
%F T(n+2,n) = A220948(n).
%F T(n+3,n) = T(n+4,n) = A224422(n). - _Philippe Deléham_, Apr 13 2013
%e Square array begins:
%e 1....1....1....1....1....1....0....0....0....0....0....0
%e 1....2....3....4....5....6....6....0....0....0....0....0
%e 1....3....6...10...15...21...27...27....0....0....0....0
%e 1....4...10...20...35...56...83..110..110....0....0....0
%e 1....5...15...35...70..126..209..319..429..429....0....0
%e 0....5...20...55..125..251..460..779.1208.1637.1637....0
%e 0....0...20...75..200..451..911.1690.2898.4535.6172.6172
%e ...
%e Square array, read by diagonals, with 0 omitted:
%e 1, 5, 20, 75, 275, 1001, 3639, 13243, 48280, ...
%e 1, 5, 20, 75, 275, 1001, 3639, 13243, 48280, ...
%e 1, 4, 15, 55, 200, 726, 2638, 9604, 35037, ...
%e 1, 3, 10, 35, 125, 451, 1637, 5965, 21794, ...
%e 1, 2, 6, 20, 70, 251, 911, 3327, 12190, 44744, ...
%e 1, 3, 10, 35, 126, 460, 1690, 6225, 22950, ...
%e 1, 4, 15, 56, 209, 779, 2898, 10760, 39882, ...
%e 1, 5, 21, 83, 319, 1208, 4535, 16932, 62986, ...
%e 1, 6, 27, 110, 429, 1637, 6172, 23104, 86090, ...
%e 1, 6, 27, 110, 429, 1637, 6172, 23104, 86090, ...
%Y Cf. Similar sequences: A214846, A216054, A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236, A216238, A217257, A217315, A217593, A217765, A217770
%K nonn,easy,tabl
%O 0,5
%A _Philippe Deléham_, Mar 30 2013