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

Author

Clark Kimberling

Keywords

• nonn
• tabl

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,...

Examples

			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)
		

Crossrefs

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

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

Programs

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 *)

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

Extensions

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