A116588 Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).
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, 32, 8, 2, 2, 8, 32, 128, 256, 64, 16, 4, 1, 4, 16, 64, 256, 512, 128, 32, 8, 2, 2, 8, 32, 128, 512, 1024, 256, 64, 16, 4, 1, 4, 16, 64, 256, 1024, 2048, 512, 128
Offset: 0
Examples
Array begins:
1 2 4 8 16 32 64 128 ...
2 1 2 4 8 16 32 64 ...
4 2 1 2 4 8 16 32 ...
8 4 2 1 2 4 8 16 ...
16 8 4 2 1 2 4 8 ...
32 16 8 4 2 1 2 4 ...
64 32 16 8 4 2 1 2 ...
128 64 32 16 8 4 2 1 ...
... reformatted and extended. - _Franck Maminirina Ramaharo_, Sep 08 2018
References
- M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford University Press, New York, 1985, p. 62.
Links
- A. Böttcher and S. M. Grudsky, Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis, Texts and Readings in Mathematics Vol. 67, 2000.
- Wikipedia, Toeplitz matrix.
Programs
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Mathematica
row[n_] := Table[Max[2^(r - q), 2^(q - r)], {r, 1, n}, {q, 1, n}]; TableForm[row[10]] (* Franck Maminirina Ramaharo, Sep 08 2018 *) -
Maxima
T(n, k) := max(2^(n - k), 2^(k - n))$ for n:0 thru 10 do (print(makelist(T(n,k), k, 0, 10))); /* Franck Maminirina Ramaharo, Sep 08 2018 */
Formula
From Franck Maminirina Ramaharo, Sep 08 2018: (Start)
G.f.: (1 - 4*x*y)/((1 - 2*x)*(1 - 2*y)*(1 - x*y)). (End)
Extensions
Edited, new name and extended by Franck Maminirina Ramaharo, Sep 08 2018
Comments