OFFSET
1,2
COMMENTS
Let the triangle = M as an infinite lower triangular matrix.
M * (1, 2, 3, ...) = A002620: (1, 2, 4, 6, 9, 12, 16, 20, ...);
M * (1, 3, 5, ...) = A084265: (1, 2, 6, 9, 15, 20, 28, 35, ...);
M * (1, 3, 6, ...) = A028724: (1, 2, 6, 9, 18, 24, 40, 50, ...);
Limit_{n->infinity} M^n = A171609: (1, 2, 4, 6, 12, 16, 24, 30, ...).
LINKS
Micah Manary, Table of n, a(n) for n = 1..5050
FORMULA
Triangle by columns, T(n,k); (..., n, (n+1)) preceded by (n-1) zeros, as an infinite lower triangular matrix.
EXAMPLE
First few rows of the triangle:
1;
2, 0;
0, 2, 0;
0, 3, 0, 0;
0, 0, 3, 0, 0;
0, 0, 4, 0, 0, 0;
0, 0, 0, 4, 0, 0, 0;
0, 0, 0, 5, 0, 0, 0, 0;
0, 0, 0, 0, 5, 0, 0, 0, 0;
0, 0, 0, 0, 6, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0;
...
MAPLE
A171609 := proc(n, k)
if k = ceil(n/2) then
floor( (n+2)/2) ;
else
0;
end if;
end proc:
seq(seq( A171609(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Sep 23 2021
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Dec 12 2009
EXTENSIONS
More terms from Micah Manary, Aug 07 2022
STATUS
approved