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%I #21 Jan 03 2023 07:21:13
%S 1,2,1,5,3,1,13,8,4,1,33,20,11,5,1,81,48,27,14,6,1,193,112,63,34,17,7,
%T 1,449,256,143,78,41,20,8,1,1025,576,319,174,93,48,23,9,1,2305,1280,
%U 703,382,205,108,55,26,10,1,5121,2816,1535,830,445,236,123,62,29,11,1
%N T(n, k) = 2^(k-1)*(k + 2*n) - n + 1, array read by descending antidiagonals.
%C Previous name was: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is k+n, for n=1,2,3,...; k=0,1,2,...
%F T(n, k) = 2^(k-1)*(k + 2*n) - n + 1. - _Benoit Cloitre_, Jun 17 2003
%F G.f.: (1 - x - 3*y + 4*x*y + 3*y^2 - 5*x*y^2)/((1 - x)^2*(1 - 2*y)^2*(1 - y)). - _Stefano Spezia_, Jan 02 2023
%e From _Stefano Spezia_, Jan 03 2023: (Start)
%e The array begins:
%e 1, 2, 5, 13, 33, 81,...
%e 1, 3, 8, 20, 48, 112,...
%e 1, 4, 11, 27, 63, 143,...
%e 1, 5, 14, 34, 78, 174,...
%e 1, 6, 17, 41, 93, 205,...
%e 1, 7, 20, 48, 108, 236,...
%e ...
%e (End)
%t T[n_,k_]:=2^(k-1)*(k+2n)-n+1;Table[Reverse[Table[T[n-k,k],{k,0,n}]],{n,0,10}]//Flatten (* _Stefano Spezia_, Jan 02 2023 *)
%Y Row 1 = (1, 2, 5, 13, 33, ...) = A005183.
%Y Row 2 = (1, 3, 8, 20, 48, ...) = A001792.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_
%E New name using formula by _Benoit Cloitre_, _Joerg Arndt_, Jan 03 2023