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A216209 Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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

MAPLE

0, seq(seq(n+k, k=0..2n), n=1..12); # Ridouane Oudra, Jun 08 2019

CROSSREFS

Cf. A051162, A094727.

Sequence in context: A256992 A261323 A134986 * A289172 A215653 A327666

Adjacent sequences:  A216206 A216207 A216208 * A216210 A216211 A216212

KEYWORD

nonn,tabf,easy

AUTHOR

Alex Ratushnyak, Mar 12 2013

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)