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,...
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
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
New name using formula by Benoit Cloitre, Joerg Arndt, Jan 03 2023
STATUS
approved