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A116588 Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).

%I A116588 #20 Sep 08 2018 11:05:43
%S A116588 1,2,2,4,1,4,8,2,2,8,16,4,1,4,16,32,8,2,2,8,32,64,16,4,1,4,16,64,128,
%T A116588 32,8,2,2,8,32,128,256,64,16,4,1,4,16,64,256,512,128,32,8,2,2,8,32,
%U A116588 128,512,1024,256,64,16,4,1,4,16,64,256,1024,2048,512,128
%N A116588 Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).
%C A116588 This array is an infinite symmetric Toeplitz matrix whose first row is the powers of two A000079. - _Franck Maminirina Ramaharo_, Sep 08 2018
%D A116588 M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford University Press, New York, 1985, p. 62.
%H A116588 A. Böttcher and S. M. Grudsky, <a href="https://dx.doi.org/10.1007/978-93-86279-04-0">Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis</a>, Texts and Readings in Mathematics Vol. 67, 2000.
%H A116588 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz matrix</a>.
%F A116588 From _Franck Maminirina Ramaharo_, Sep 08 2018: (Start)
%F A116588 T(n,k) = A130321(n,k) for 0 <= k <= n and A130321(k,n) otherwise.
%F A116588 G.f.: (1 - 4*x*y)/((1 - 2*x)*(1 - 2*y)*(1 - x*y)). (End)
%e A116588 Array begins:
%e A116588     1   2   4   8  16  32  64  128 ...
%e A116588     2   1   2   4   8  16  32   64 ...
%e A116588     4   2   1   2   4   8  16   32 ...
%e A116588     8   4   2   1   2   4   8   16 ...
%e A116588    16   8   4   2   1   2   4    8 ...
%e A116588    32  16   8   4   2   1   2    4 ...
%e A116588    64  32  16   8   4   2   1    2 ...
%e A116588   128  64  32  16   8   4   2    1 ...
%e A116588   ... reformatted and extended. - _Franck Maminirina Ramaharo_, Sep 08 2018
%t A116588 row[n_] := Table[Max[2^(r - q), 2^(q - r)], {r, 1, n}, {q, 1, n}];
%t A116588 TableForm[row[10]] (* _Franck Maminirina Ramaharo_, Sep 08 2018 *)
%o A116588 (Maxima)
%o A116588 T(n, k) := max(2^(n - k), 2^(k - n))$
%o A116588 for n:0 thru 10 do (print(makelist(T(n,k), k, 0, 10))); /* _Franck Maminirina Ramaharo_, Sep 08 2018 */
%Y A116588 Antidiagonal sums: A084639.
%Y A116588 Cf. A082693, A130321.
%K A116588 nonn,easy,tabl
%O A116588 0,2
%A A116588 _Roger L. Bagula_, Mar 27 2006
%E A116588 Edited, new name and extended by _Franck Maminirina Ramaharo_, Sep 08 2018