OFFSET
1,1
LINKS
G. C. Greubel, Rows n=0..100 of the triangle, flattened
S. Helgason, A Centennial: Wilhelm Killing and the Exceptional Groups, Mathematical Intelligencer 12, no. 3 (1990). [See p. 3.]
FORMULA
T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.
EXAMPLE
Triangle begins as:
5;
15, 16;
27, 28, 29;
41, 42, 43, 44;
57, 58, 59, 60, 61;
75, 76, 77, 78, 79, 80;
MATHEMATICA
T[n_, k_]:= If[n==0 && k==0, 5, If[k==0 && n==1, 15, n*(n+9) +k +5]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Sage)
@CachedFunction
def T(n, k):
if (n==0 and k==0): return 5
elif (k==0 and n==1): return 15
else: return n*(n + 9) + k + 5
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 05 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, May 06 2007
EXTENSIONS
More terms and edits by G. C. Greubel, Feb 05 2021
STATUS
approved