A134483 Triangle read by rows: T(n,k) = 2n + k - 2; 1 <= k <= n.

1, 3, 4, 5, 6, 7, 7, 8, 9, 10, 9, 10, 11, 12, 13, 11, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 21, 22, 17, 18, 19, 20, 21, 22, 23, 24, 25, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28

Offset

1,2

Comments

Row sums are the heptagonal numbers, A000566: (1, 7, 18, 34, 55, 81, ...).

Row n consists of n consecutive integers starting with 2n-1. - Emeric Deutsch, Nov 04 2007

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

From Emeric Deutsch, Nov 04 2007: (Start)

T(n,k) = 2n + k - 2 for 1 <= k <= n.

G.f. = t*z(1 + z + 2*t*z - 4*t*z^2)/((1-z)^2*(1-t*z)^2). (End)

From Boris Putievskiy, Jan 16 2013: (Start)

a(n) = A002260(n) + 2*A003056(n);

a(n) = j+2*t, where j = n - t*(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). (End)

Example

First few rows of the triangle:
  1;
  3,  4;
  5,  6,  7;
  7,  8,  9, 10;
  9, 10, 11, 12, 13;
  ...

Maple

for n to 10 do seq(2*n+k-2, k=1..n) end do; # yields sequence in triangular form - Emeric Deutsch, Nov 04 2007

Mathematica

Table[2n+k-2, {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Oct 14 2022 *)

Crossrefs

Cf. A000566.

Cf. A002260, A003056.

Sequence in context: A196119 A225852 A198458 * A121151 A088243 A154660

Adjacent sequences: A134480 A134481 A134482 * A134484 A134485 A134486

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 27 2007

Status

approved