A279891 Triangle read by rows, T(n,k) = 2*n, with n>=k>=0.

0, 2, 2, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset

0,2

Comments

2*n appears n+1 times in row n.

Links

Table of n, a(n) for n=0..77.

Formula

a(n) = 2*floor((sqrt(1+8*n)-1)/2).

a(n) = 2*A003056(n) = 2*(A002024(n+1)-1).

Example

Triangle begins:
0;
2,  2;
4,  4,  4;
6,  6,  6,  6;
8,  8,  8,  8,  8;
10, 10, 10, 10, 10, 10;
12, 12, 12, 12, 12, 12, 12;
14, 14, 14, 14, 14, 14, 14, 14;
16, 16, 16, 16, 16, 16, 16, 16, 16;
18, 18, 18, 18, 18, 18, 18, 18, 18, 18;
20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20;
22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22;
...

Mathematica

Table[ConstantArray[2 n, n + 1], {n, 0, 11}] // Flatten (* Michael De Vlieger, Dec 22 2016 *)
Table[#, #/2+1]&/@(2*Range[0, 20])//Flatten(* Harvey P. Dale, Oct 09 2018 *)

Prog

(PARI) row(n) = vector(n, x, 2*(n-1))
trianglerows(n) = for(k=1, n, print(row(k)))
/* Print initial 12 rows of triangle as follows: */
trianglerows(12) \\ Felix Fröhlich, Dec 22 2016

Crossrefs

Twice A003056.

Row sums give A046092.

Where records occur gives A000217.

Column 0, and the right border: A005843.

Also row lengths of the following triangles: A237593, A262045, A262048, A279693.

Cf. A002024.

Sequence in context: A265263 A113320 A085237 * A110870 A206224 A035114

Adjacent sequences: A279888 A279889 A279890 * A279892 A279893 A279894

Keyword

nonn,tabl,easy

Author

Omar E. Pol, Dec 22 2016

Status

approved