A141429 Triangle T(n, k) = (k+1)*(n-k+1), read by rows.

2, 4, 3, 6, 6, 4, 8, 9, 8, 5, 10, 12, 12, 10, 6, 12, 15, 16, 15, 12, 7, 14, 18, 20, 20, 18, 14, 8, 16, 21, 24, 25, 24, 21, 16, 9, 18, 24, 28, 30, 30, 28, 24, 18, 10, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13

Offset: 1

Author

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

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins as:
   2;
   4,  3;
   6,  6,  4;
   8,  9,  8,  5;
  10, 12, 12, 10,  6;
  12, 15, 16, 15, 12,  7;
  14, 18, 20, 20, 18, 14,  8;
  16, 21, 24, 25, 24, 21, 16,  9;
  18, 24, 28, 30, 30, 28, 24, 18, 10;
  20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
		

Links

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

Crossrefs

Cf. A003991, A004247, A005581, A144329, A158823.

Programs

Magma

[(k+1)*(n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 30 2021

Maple

A141429 := proc(n,k)
        (k+1)*(n-k+1) ;
end proc:
seq(seq(A141429(n,m),m=1..n),n=1..14) ; # R. J. Mathar, Nov 10 2011

Mathematica

Table[(k+1)*(n-k+1), {n,15}, {k,n}]//Flatten

Sage

flatten([[(k+1)*(n-k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 30 2021

Formula

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

T(n, k) = A158823(n+2, k+2).

Sum_{k=1..n} T(n, k) = A005581(n+1).

Extensions

Edited by G. C. Greubel, Mar 30 2021