%I #16 Feb 06 2021 08:51:57

%S 5,15,16,27,28,29,41,42,43,44,57,58,59,60,61,75,76,77,78,79,80,95,96,

%T 97,98,99,100,101,117,118,119,120,121,122,123,124,141,142,143,144,145,

%U 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

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

%H G. C. Greubel, <a href="/A109161/b109161.txt">Rows n=0..100 of the triangle, flattened</a>

%H S. Helgason, <a href="https://web.archive.org/web/20060913232213/http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-755Fall-2004/12BE03CD-1B28-41C6-8D2A-85097D4EEB68/0/helgacentSTD.pdf">A Centennial: Wilhelm Killing and the Exceptional Groups</a>, Mathematical Intelligencer 12, no. 3 (1990). [See p. 3.]

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

%e Triangle begins as:

%e 5;

%e 15, 16;

%e 27, 28, 29;

%e 41, 42, 43, 44;

%e 57, 58, 59, 60, 61;

%e 75, 76, 77, 78, 79, 80;

%t T[n_, k_]:= If[n==0 && k==0, 5, If[k==0 && n==1, 15, n*(n+9) +k +5]];

%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (n==0 and k==0): return 5

%o elif (k==0 and n==1): return 15

%o else: return n*(n + 9) + k + 5

%o flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Feb 05 2021

%Y Cf. A106373, A106374, A106403.

%K nonn,tabl,easy,less

%O 1,1

%A _Roger L. Bagula_, May 06 2007

%E More terms and edits by _G. C. Greubel_, Feb 05 2021