A047858 T(n, k) = 2^(k-1)*(k + 2*n) - n + 1, array read by descending antidiagonals.

1, 2, 1, 5, 3, 1, 13, 8, 4, 1, 33, 20, 11, 5, 1, 81, 48, 27, 14, 6, 1, 193, 112, 63, 34, 17, 7, 1, 449, 256, 143, 78, 41, 20, 8, 1, 1025, 576, 319, 174, 93, 48, 23, 9, 1, 2305, 1280, 703, 382, 205, 108, 55, 26, 10, 1, 5121, 2816, 1535, 830, 445, 236, 123, 62, 29, 11, 1

Offset

0,2

Comments

Previous name was: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is k+n, for n=1,2,3,...; k=0,1,2,...

Links

Table of n, a(n) for n=0..65.

Formula

T(n, k) = 2^(k-1)*(k + 2*n) - n + 1. - Benoit Cloitre, Jun 17 2003

G.f.: (1 - x - 3*y + 4*x*y + 3*y^2 - 5*x*y^2)/((1 - x)^2*(1 - 2*y)^2*(1 - y)). - Stefano Spezia, Jan 02 2023

Example

From Stefano Spezia, Jan 03 2023: (Start)
The array begins:
  1, 2,  5, 13,  33,  81,...
  1, 3,  8, 20,  48, 112,...
  1, 4, 11, 27,  63, 143,...
  1, 5, 14, 34,  78, 174,...
  1, 6, 17, 41,  93, 205,...
  1, 7, 20, 48, 108, 236,...
  ...
(End)

Mathematica

T[n_, k_]:=2^(k-1)*(k+2n)-n+1; Table[Reverse[Table[T[n-k, k], {k, 0, n}]], {n, 0, 10}]//Flatten (* Stefano Spezia, Jan 02 2023 *)

Crossrefs

Row 1 = (1, 2, 5, 13, 33, ...) = A005183.

Row 2 = (1, 3, 8, 20, 48, ...) = A001792.

Sequence in context: A054446 A164981 A366858 * A125171 A280784 A048472

Adjacent sequences: A047855 A047856 A047857 * A047859 A047860 A047861

Keyword

nonn,tabl

Author

Clark Kimberling

Extensions

New name using formula by Benoit Cloitre, Joerg Arndt, Jan 03 2023

Status

approved