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A205456 Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1.

%I A205456 #7 Mar 30 2012 18:58:11
%S A205456 1,2,2,3,1,3,4,3,3,4,5,6,1,6,5,6,10,4,4,10,6,7,15,10,1,10,15,7,8,21,
%T A205456 20,5,5,20,21,8,9,28,35,15,1,15,35,28,9,10,36,56,35,6,6,35,56,36,10,
%U A205456 11,45,84,70,21,1,21,70,84,45,11,12,55,120,126,56,7,7,56,126,120
%N A205456 Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1.
%C A205456 C(max(i,j),min(i,j))=number of {E,N,NE} paths from (0,0) to (i,j).  Each step of a path is represented by (a,b)->(a+1,b) or (a,b)->(a,b+1) or (a,b)->(a+1,b+1).  To include paths from (0,0) to points (a,0) and (0,b), see A059674.
%e A205456 Northwest corner:
%e A205456 1....2....3....4....5....6....7
%e A205456 2....1....3....6....10...15...21
%e A205456 3....3....1....4....10...20...35
%e A205456 4....6....4....1....5....15...35
%e A205456 5....10...10...5....1....6....21
%t A205456 f[i_, j_] := Binomial[Max[i, j], Min[i, j]]
%t A205456 TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A205456 Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]
%Y A205456 Cf. A205457, A205548, A059674.
%K A205456 nonn,tabl
%O A205456 1,2
%A A205456 _Clark Kimberling_, Jan 28 2012