A134061 Triangle read by rows: T(n,k) = A124928(n,k) + A134059(n,k) - A007318(n,k).

1, 3, 5, 3, 10, 5, 3, 15, 15, 5, 3, 20, 30, 20, 5, 3, 25, 50, 50, 25, 5, 3, 30, 75, 100, 75, 30, 5, 3, 35, 105, 175, 175, 105, 35, 5, 3, 40, 140, 280, 350, 280, 140, 40, 5, 3, 45, 180, 420, 630, 630, 420, 180, 45, 5, 3, 50, 225, 600, 1050, 1260, 1050, 600, 225, 50, 5

Offset

0,2

Comments

Row sums = A134062: (1, 8, 18, 38, 78, 158, ...).

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = 5*binomial(n,k) if k > 0, (0 <= k <= n), with leftmost column = (1,3,3,3,...).

Example

First few rows of the triangle:
  1;
  3,  5;
  3, 10,  5;
  3, 15, 15,  5;
  3, 20, 30, 20,  5;
  3, 25, 50, 50, 25,  5;
  ...

Mathematica

Table[If[k > 0, 3*Binomial[n, k], 1] + 2*Binomial[n, k] - 2*Boole[n == 0], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 31 2025 *)

Crossrefs

Cf. A007318, A124928, A134059, A134062 (row sums).

Sequence in context: A070554 A076842 A077862 * A336872 A167221 A177930

Adjacent sequences: A134058 A134059 A134060 * A134062 A134063 A134064

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Oct 05 2007

Extensions

More terms from Amiram Eldar, May 31 2025

Status

approved