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A134060 Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 23:42 EDT 2021. Contains 347673 sequences. (Running on oeis4.)