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A116588 Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)). 0

%I

%S 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 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 128,512,1024,256,64,16,4,1,4,16,64,256,1024,2048,512,128

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

%C This array is an infinite symmetric Toeplitz matrix whose first row is the powers of two A000079. - _Franck Maminirina Ramaharo_, Sep 08 2018

%D M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford University Press, New York, 1985, p. 62.

%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz matrix</a>.

%F From _Franck Maminirina Ramaharo_, Sep 08 2018: (Start)

%F T(n,k) = A130321(n,k) for 0 <= k <= n and A130321(k,n) otherwise.

%F G.f.: (1 - 4*x*y)/((1 - 2*x)*(1 - 2*y)*(1 - x*y)). (End)

%e Array begins:

%e 1 2 4 8 16 32 64 128 ...

%e 2 1 2 4 8 16 32 64 ...

%e 4 2 1 2 4 8 16 32 ...

%e 8 4 2 1 2 4 8 16 ...

%e 16 8 4 2 1 2 4 8 ...

%e 32 16 8 4 2 1 2 4 ...

%e 64 32 16 8 4 2 1 2 ...

%e 128 64 32 16 8 4 2 1 ...

%e ... reformatted and extended. - _Franck Maminirina Ramaharo_, Sep 08 2018

%t row[n_] := Table[Max[2^(r - q), 2^(q - r)], {r, 1, n}, {q, 1, n}];

%t TableForm[row[10]] (* _Franck Maminirina Ramaharo_, Sep 08 2018 *)

%o (Maxima)

%o T(n, k) := max(2^(n - k), 2^(k - n))$

%o for n:0 thru 10 do (print(makelist(T(n,k), k, 0, 10))); /* _Franck Maminirina Ramaharo_, Sep 08 2018 */

%Y Antidiagonal sums: A084639.

%Y Cf. A082693, A130321.

%K nonn,easy,tabl

%O 0,2

%A _Roger L. Bagula_, Mar 27 2006

%E Edited, new name and extended by _Franck Maminirina Ramaharo_, Sep 08 2018

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Last modified June 19 13:21 EDT 2021. Contains 345138 sequences. (Running on oeis4.)