A109161 Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.

5, 15, 16, 27, 28, 29, 41, 42, 43, 44, 57, 58, 59, 60, 61, 75, 76, 77, 78, 79, 80, 95, 96, 97, 98, 99, 100, 101, 117, 118, 119, 120, 121, 122, 123, 124, 141, 142, 143, 144, 145, 146, 147, 148, 149, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205

Offset: 1

Author

Roger L. Bagula, May 06 2007

Keywords

• nonn
• tabl
• easy
• less

Examples

			Triangle begins as:
   5;
  15, 16;
  27, 28, 29;
  41, 42, 43, 44;
  57, 58, 59, 60, 61;
  75, 76, 77, 78, 79, 80;
		

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.]

Crossrefs

Cf. A106373, A106374, A106403.

Programs

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

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

Formula

T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.

Extensions

More terms and edits by G. C. Greubel, Feb 05 2021