A134480 Triangle read by rows: T(n,k) = Sum_{i=k..n} n + i.

0, 3, 2, 9, 7, 4, 18, 15, 11, 6, 30, 26, 21, 15, 8, 45, 40, 34, 27, 19, 10, 63, 57, 50, 42, 33, 23, 12, 84, 77, 69, 60, 50, 39, 27, 14, 108, 100, 91, 81, 70, 58, 45, 31, 16, 135, 126, 116, 105, 93, 80, 66, 51, 35, 18, 165, 155, 144, 132, 119, 105, 90, 74, 57, 39, 20

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

Equals A051162 * A000012 as infinite lower triangular matrices.

From Andrew Howroyd, Sep 20 2025: (Start)

T(n,k) = n*(2*n + 1) - (n + k)*(n + k - 1)/2

G.f.: x*(3 + 2*y - 5*y*x)/((1 - x)^3*(1 - y*x)^2). (End)

Example

First few rows of the triangle:
   0;
   3,  2;
   9,  7,  4;
  18, 15, 11,  6;
  30, 26, 21, 15,  8;
  45, 40, 34, 27, 19, 10;
  63, 57, 50, 42, 33, 23, 12;
  ...

Crossrefs

Row sums are A134481.

Column k=0 is A045943.

Main diagonal is A005843.

Cf. A051162.

Sequence in context: A346109 A362220 A019778 * A182950 A011323 A227630

Adjacent sequences: A134477 A134478 A134479 * A134481 A134482 A134483

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 27 2007

Extensions

Definition edited, a(0) changed to 0 and a(55) onwards from Andrew Howroyd, Sep 20 2025

Status

approved