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

1,1

Links

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

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).

Example

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;

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

Prog

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

Crossrefs

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

Sequence in context: A245454 A375615 A143273 * A309131 A162953 A235451

Adjacent sequences: A141426 A141427 A141428 * A141430 A141431 A141432

Keyword

nonn,easy,tabl

Author

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

Extensions

Edited by G. C. Greubel, Mar 30 2021

Status

approved