A132923 Triangle read by rows: T(n, k) = Fibonacci(k) + n - k.

1, 2, 1, 3, 2, 2, 4, 3, 3, 3, 5, 4, 4, 4, 5, 6, 5, 5, 5, 6, 8, 7, 6, 6, 6, 7, 9, 13, 8, 7, 7, 7, 8, 10, 14, 21, 9, 8, 8, 8, 9, 11, 15, 22, 34, 10, 9, 9, 9, 10, 12, 16, 23, 35, 55, 11, 10, 10, 10, 11, 13, 17, 24, 36, 56, 89, 12, 11, 11, 11, 12, 14, 18, 25, 37, 57, 90, 144

Offset

1,2

Comments

Row sums give A081662.

Right border is A000045.

Old name was: Triangle by columns, F(n) followed by (F(n)+1), (F(n)+2), (F(n)+3), ...

Links

David A. Corneth, Table of n, a(n) for n = 1..10011

Formula

T(k, k) = Fibonacci(k). T(k + n, k) = T(k, k) + n. - David A. Corneth, Feb 14 2023

Example

First few rows of the triangle:
  1;
  2, 1;
  3, 2, 2;
  4, 3, 3, 3;
  5, 4, 4, 4, 5;
  6, 5, 5, 5, 6, 8;
  7, 6, 6, 6, 7, 9, 13;
  ...

Mathematica

T[n_, k_]:=n+Fibonacci[k]-k; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* James C. McMahon, Mar 09 2025 *)

Prog

(PARI) T(n, k) = fibonacci(k) + n - k \\ David A. Corneth, Feb 14 2023

Crossrefs

Cf. A000045, A081662.

Sequence in context: A317207 A102364 A342774 * A390879 A144329 A141157

Adjacent sequences: A132920 A132921 A132922 * A132924 A132925 A132926

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 05 2007

Extensions

More terms from and new name by David A. Corneth, Feb 14 2023

Status

approved