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

0,3

Comments

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

Links

Table of n, a(n) for n=0..63.

Eric Naslund, Euler-Mascheroni constant expression, further simplification

Formula

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

Example

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

Maple

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

Crossrefs

Cf. A051162, A094727.

Sequence in context: A261323 A134986 A336860 * A289172 A215653 A358503

Adjacent sequences: A216206 A216207 A216208 * A216210 A216211 A216212

Keyword

nonn,tabf,easy

Author

Alex Ratushnyak, Mar 12 2013

Status

approved