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%I #19 Apr 09 2013 12:08:33
%S 0,2,1,2,3,1,4,3,3,2,6,5,3,4,3,10,7,5,4,5,5,16,11,7,6,5,7,8,26,17,11,
%T 8,7,7,10,13,42,27,17,12,9,9,10,15,21,68,43,27,18,13,11,12,15,23,34,
%U 110,69,43,28,19,15,14,17,23,36,55,178,111,69,44,29,21
%N Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.
%F T(n,0) = A000045(n).
%F T(1,k) = A001588(k).
%F T(n,1) = T(n,2) = A157725(n).
%F T(n,3) = A157727(n).
%F T(n,n)= A022086(n) = 3*A000045(n).
%F T(n+1,n) = A000032(n+1) = A000204(n+1).
%F T(n+2,n) = A000285(n).
%F T(n+3,n) = A013655(n+1) = A001060(n+1).
%F T(n+4,n) = A021120(n).
%F T(n+5,n) = A022088(n+2) = 5*A000045(n+2).
%F T(n+6,n) = A022097(n+2).
%F T(n+7,n) = A022122(n+2).
%F T(n+8,n) = 3*A013655(n+2).
%F T(n+9,n) = A097657(n+2).
%F T(n+10,n) = A022118(n+4).
%F T(n,n+1) = A000045(n+3).
%F T(n,n+2) = A013655(n+1) = A001060(n+1).
%F T(n,n+3) = A000032(n+3).
%F T(n,n+4) = A022095(n+2).
%F T(n,n+5) = A022120(n+2).
%F T(n,n+6) = A022136(n+2).
%F T(n,n+7) = A022098(n+4).
%F T(n,n+8) = A022380(n+4).
%F T(n,n+9) = A206419(n+6).
%F Sum(T(n-k,k), 0<=k<=n) = 3*A000071(n+2).
%e Square array begins:
%e ...0....2....2....4....6...10...16...26...42...
%e ...1....3....3....5....7...11...17...27...43...
%e ...1....3....3....5....7...11...17...27...43...
%e ...2....4....4....6....8...12...18...28...44...
%e ...3....5....5....7....9...13...19...29...45...
%e ...5....7....7....9...11...15...21...31...47...
%e ...8...10...10...12...14...18...24...34...50...
%e ..13...15...15...17...19...23...29...39...55...
%e ..21...23...23...25...27...31...37...47...63...
%e ..34...36...36...38...40...44...50...60...76...
%e ..55...57...57...59...61...65...71...81...97...
%e ..89...91...91...93...95...99..105..115..131...
%e .144..146..146..148..150..154..160..170..186...
%e ...
%Y Cf. A000045
%K nonn,tabl
%O 0,2
%A _Philippe Deléham_, Apr 07 2013