A094727 -id:A094727 - cp's OEIS frontend

A216209 Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n.

0, 1, 2, 3, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 11, 12, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Offset: 0

Alex Ratushnyak, Mar 12 2013

The left half together with the central column is the A051162 triangle.
Row sums of the reciprocals of the terms in the above triangle converge to log(3). See link to Eric Naslund's answer. [Mats Granvik, Apr 07 2013]
The first time that the numbers of the triplet 3k+1, 3k+2, 3k+3 appear in the sequence is for a(k^2+4*k+1) = 3*k+1, a(k^2+4*k+2) = 3*k+2, a(k^2+4*k+3) = 3*k+3 for k >= 0. - Bernard Schott, Jun 09 2019

			Triangle begins:
                     0
                  1  2  3
               2  3  4  5  6
            3  4  5  6  7  8  9
         4  5  6  7  8  9 10 11 12
      5  6  7  8  9 10 11 12 13 14 15
   6  7  8  9 10 11 12 13 14 15 16 17 18
7  8  9 10 11 12 13 14 15 16 17 18 19 20 21

Eric Naslund, Euler-Mascheroni constant expression, further simplification

Cf. A051162, A094727.

seq(seq(n+k, k=0..2*n), n=0..12); # Ridouane Oudra, Jun 08 2019

a(n) = floor(sqrt(n)) - floor(sqrt(n))^2 + n. - Ridouane Oudra, Jun 08 2019

cp's OEIS Frontend

A216209 Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n.

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