A082693 -id:A082693 - cp's OEIS frontend

A082694 Partial sums of A082693.

1, 3, 4, 6, 10, 12, 13, 15, 19, 27, 31, 33, 34, 36, 40, 48, 64, 72, 76, 78, 79, 81, 85, 93, 109, 141, 157, 165, 169, 171, 172, 174, 178, 186, 202, 234, 298, 330, 346, 354, 358, 360, 361, 363, 367, 375, 391, 423, 487, 615, 679, 711, 727, 735, 739, 741, 742, 744

Offset: 1

Benoit Cloitre, Apr 12 2003

nonn

f[n_]:=Module[{st=2^Range[0,n]},Join[st,Reverse[Most[Rest[st]]]]]; Accumulate[ Flatten[Array[f,10]]] (* Harvey P. Dale, May 09 2012 *)

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

Original entry on oeis.org

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

Roger L. Bagula, Mar 27 2006

This array is an infinite symmetric Toeplitz matrix whose first row is the powers of two A000079. - Franck Maminirina Ramaharo, Sep 08 2018

			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

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

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.

Antidiagonal sums: A084639.

Cf. A082693, A130321.

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 *)

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 */

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)

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

cp's OEIS Frontend

A082694 Partial sums of A082693.

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

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