OFFSET
1,2
LINKS
Stefano Spezia, First 150 rows of the triangle, flattened
FORMULA
As an infinite lower triangular matrix, (1, 3, 5, ...) in the main diagonal and (2, 4, 6, ...) in the subdiagonal; with the rest zeros.
From Stefano Spezia, Dec 21 2021: (Start)
T(n, k) = 2*n - 1 if n = k, T(n, k) = 2*(n - 1) if n - k = 1, otherwise T(n, k) = 0.
G.f.: x*y*(1 + x*(2 + y))/(1 - x*y)^2. (End)
EXAMPLE
First few rows of the triangle are:
1;
2, 3;
0, 4, 5;
0, 0, 6, 7;
0, 0, 0, 8, 9;
0, 0, 0, 0, 10, 11;
...
MATHEMATICA
T[n_, k_]:=If[n==k, 2n-1, If[n-k==1, 2(n-1), 0]]; Flatten[Table[T[n, k], {n, 12}, {k, n}]] (* Stefano Spezia, Dec 21 2021 *)
Join[{1}, Flatten[{#, PadRight[{}, #[[1]]/2, 0]}&/@Partition[Range[2, 30], 2]]] (* Harvey P. Dale, Mar 24 2024 *)
Join[{1}, Flatten[Table[Join[Range[2n, 2n+1], PadRight[{}, n, 0]], {n, 20}]]] (* Harvey P. Dale, Mar 25 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Aug 28 2007
EXTENSIONS
More terms from Stefano Spezia, Dec 21 2021
STATUS
approved