A134226 Triangle T(n, k) = 3*n - 4 if k = n-1 otherwise k, read by rows.

1, 2, 2, 1, 5, 3, 1, 2, 8, 4, 1, 2, 3, 11, 5, 1, 2, 3, 4, 14, 6, 1, 2, 3, 4, 5, 17, 7, 1, 2, 3, 4, 5, 6, 20, 8, 1, 2, 3, 4, 5, 6, 7, 23, 9, 1, 2, 3, 4, 5, 6, 7, 8, 26, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 29, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 32, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 35, 13

Offset

1,2

Links

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

Formula

T(n, k) = A134082(n, k) + A002260(n, k) - I, an infinite lower triangular matrix and I = Identity matrix.

From G. C. Greubel, Feb 17 2021: (Start)

T(n, k) = 3*n - 4 if k = n-1 otherwise k.

Sum_{k=1..n} T(n, k) = A134227(n) = (n-1)*(n+6)/2 + [n=1]. (End)

Example

First few rows of the triangle are:
  1;
  2, 2;
  1, 5, 3;
  1, 2, 8,  4;
  1, 2, 3, 11,  5;
  1, 2, 3,  4, 14,  6;
  1, 2, 3,  4,  5, 17, 7;
  ...

Mathematica

T[n_, k_]:= If[k==n-1, 3*n-4, k];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *)

Prog

(Sage)
def A134226(n, k): return 3*n-4 if k==n-1 else k
flatten([[A134226(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Feb 17 2021
(Magma)
A134226:= func< n, k | k eq n-1 select 3*n-4 else k >;
[A134226(n, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Feb 17 2021

Crossrefs

Cf. A002260, A134082, A134227.

Sequence in context: A102849 A088333 A016538 * A184050 A367094 A324798

Adjacent sequences: A134223 A134224 A134225 * A134227 A134228 A134229

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 14 2007

Extensions

New name and more terms added by G. C. Greubel, Feb 17 2021

Status

approved