A141432 Triangle T(n,k) = (k+1)*(n-k-1) read by rows.

-2, 0, -3, 2, 0, -4, 4, 3, 0, -5, 6, 6, 4, 0, -6, 8, 9, 8, 5, 0, -7, 10, 12, 12, 10, 6, 0, -8, 12, 15, 16, 15, 12, 7, 0, -9, 14, 18, 20, 20, 18, 14, 8, 0, -10, 16, 21, 24, 25, 24, 21, 16, 9, 0, -11

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Aug 06 2008

Keywords

• tabl
• easy
• sign

Examples

			Triangle begins as:
  -2;
   0, -3;
   2,  0, -4;
   4,  3,  0, -5;
   6,  6,  4,  0, -6;
   8,  9,  8,  5,  0, -7;
  10, 12, 12, 10,  6,  0, -8;
  12, 15, 16, 15, 12,  7,  0, -9;
  14, 18, 20, 20, 18, 14,  8,  0, -10;
  16, 21, 24, 25, 24, 21, 16,  9,   0, -11;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A003991, A004247.

Programs

Magma

[(k+1)*(n-k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2021

Maple

A141432:= (n,k) -> (k+1)*(n-k-1); seq(seq(A141432(n,k), k=1..n), n=1..12); # G. C. Greubel, Apr 01 2021

Mathematica

Table[(k+1)*(n-k-1), {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 01 2021 *)

Sage

flatten([[(k+1)*(n-k-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 01 2021

Formula

T(n,k) = (k+1)*(n-k-1).

Sum_{k=1..n} T(n, k) = n*(n^2 - 13)/6.

G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = (2*x-1-y)/((1-y)^3*(x-1)^2). - R. J. Mathar, Feb 19 2020