OFFSET
1,2
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = A004736(n, k) + A134081(n, k) - I, an infinite lower triangular matrix, where I = Identity matrix.
From G. C. Greubel, Feb 17 2021: (Start)
T(n, k) = n - k + 1 with T(n, n-1) = 2*n - 1 and T(n, n) = 1.
Sum_{k=1..n} T(n, k) = (n-1)*(n+6)/2 + [n=1] = A134227(n). (End)
EXAMPLE
First few rows of the triangle are:
1;
3, 1;
3, 5, 1;
4, 3, 7, 1;
5, 4, 3, 9, 1;
6, 5, 4, 3, 11, 1;
7, 6, 5, 4, 3, 13, 1;
...
MATHEMATICA
T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n-1, n-k+1]];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *)
PROG
(Sage)
def A134231(n, k): return 1 if k==n else 2*n-1 if k==n-1 else n-k+1
flatten([[A134231(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Feb 17 2021
(Magma)
A134231:= func< n, k | k eq n select 1 else k eq n-1 select 2*n-1 else n-k+1 >;
[A134231(n, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Feb 17 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Oct 14 2007
EXTENSIONS
More terms and title changed by G. C. Greubel, Feb 17 2021
STATUS
approved