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

0,2

Comments

This array is an infinite symmetric Toeplitz matrix whose first row is the powers of two A000079. - 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

Table of n, a(n) for n=0..68.

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.

Formula

From Franck Maminirina Ramaharo, Sep 08 2018: (Start)

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

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

Example

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

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 *)

Prog

(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 */

Crossrefs

Antidiagonal sums: A084639.

Cf. A082693, A130321.

Sequence in context: A111580 A066202 A027420 * A069922 A072211 A360825

Adjacent sequences: A116585 A116586 A116587 * A116589 A116590 A116591

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Mar 27 2006

Extensions

Edited, new name and extended by Franck Maminirina Ramaharo, Sep 08 2018

Status

approved