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A047858
T(n, k) = 2^(k-1)*(k + 2*n) - n + 1, array read by descending antidiagonals.
11
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,...
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
KEYWORD
nonn,tabl
EXTENSIONS
New name using formula by Benoit Cloitre, Joerg Arndt, Jan 03 2023
STATUS
approved