A134060 Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows.

1, 2, 3, 2, 6, 3, 2, 9, 9, 3, 2, 12, 18, 12, 3, 2, 15, 30, 30, 15, 3, 2, 18, 45, 60, 45, 18, 3, 2, 21, 63, 105, 105, 63, 21, 3, 2, 24, 84, 168, 210, 168, 84, 24, 3, 2, 27, 108, 252, 378, 378, 252, 108, 27, 3

Offset

0,2

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k) as infinite lower triangular matrices.

Sum_{k=0..n} T(n, k) = A052940(n).

T(n, k) = 3*binomial(n,k) - [k=0] - [n=0]. - G. C. Greubel, May 03 2021

Example

First few rows of the triangle are:
  1;
  2,  3;
  2,  6,  3;
  2,  9,  9,  3;
  2, 12, 18, 12,  3;
  2, 15, 30, 30, 15, 3;
  ...

Mathematica

Table[3*Binomial[n, k] -Boole[k==0] -Boole[n==0], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, May 03 2021 *)

Prog

(Magma) [1] cat [k eq 0 select 2 else 3*Binomial(n, k): k in [0..n], n in [1..12]]; // G. C. Greubel, May 03 2021
(Sage)
def A134060(n, k): return 3*binomial(n, k) -bool(k==0) -bool(n==0)
flatten([[A134060(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021

Crossrefs

Cf. A007318, A052940 (row sums), A127927, A134058.

Sequence in context: A183105 A316608 A033031 * A329282 A197289 A161888

Adjacent sequences: A134057 A134058 A134059 * A134061 A134062 A134063

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 05 2007

Status

approved