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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 (list; table; graph; refs; listen; history; text; internal format)
 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. BĂ¶ttcher 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 A328925 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

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Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)