OFFSET
1,2
COMMENTS
Right border = tetrahedral numbers, left border = triangular numbers.
Alternatively this is the square array A(n,k)
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...
10, 19, 31, 46, 64, 85, 109, 136, 166, 199, ...
20, 34, 52, 74, 100, 130, 164, 202, 244, 290, ...
35, 55, 80, 110, 145, 185, 230, 280, 335, 395, ...
56, 83, 116, 155, 200, 251, 308, 371, 440, 515, ...
...
read by antidiagonals where A(n,k) = n*(n^2 + 3*k*n + 3*k^2 - 1)/6 is the sum of n triangular numbers starting at A000217(k). - R. J. Mathar, May 06 2015
FORMULA
T(n,k) = k*(k^2-3*k*n-3*k+3*n^2+6*n+2) / 6. - R. J. Mathar, Aug 31 2022
EXAMPLE
First few rows of the triangle:
1;
3, 4;
6, 9, 10;
10, 16, 19, 20;
15, 25, 31, 34, 35;
21, 36, 46, 52, 55, 56;
28, 49, 64, 74, 80, 83, 84;
36, 64, 85, 100, 110, 116, 119, 120;
...
MAPLE
A143037 := proc(n, k)
k*(k^2-3*k*n-3*k+3*n^2+6*n+2) / 6 ;
end proc:
seq(seq(A143037(n, k), k=1..n), n=1..12) ; # R. J. Mathar, Aug 31 2022
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson & Roger L. Bagula, Jul 18 2008
STATUS
approved