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A116588
Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).
0
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
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.
Sequence in context: A111580 A066202 A027420 * A069922 A072211 A360825
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