A132919 Triangle read by rows: T(n,k) = Fibonacci(n) + k - 1.

1, 1, 2, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 34, 35, 36, 37, 38, 39, 40, 41, 42, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Offset: 1

Author

Gary W. Adamson, Sep 05 2007

Keywords

• nonn
• tabl

Comments

Left border = Fibonacci numbers, right border = A081659.

Infinite lower triangular matrix by rows: n-th row = n terms of: F(n) followed by (F(n) + 1), (F(n) + 2), (F(n) + 3), ...

Examples

			First few rows of the triangle:
  1;
  1,  2;
  2,  3,  4;
  3,  4,  5,  6;
  5,  6,  7,  8,  9;
  8,  9, 10, 11, 12, 13;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Crossrefs

Row sums are A132920.

Cf. A127647, A127648, A081659, A000045.

Cf. A132921, A132923.

Programs

Mathematica

T[n_,k_]:=Fibonacci[n]+k-1;Table[T[n,k],{n,11},{k,n}]//Flatten (* James C. McMahon, Mar 09 2025 *)

PARI

T(n,k) = if(k<=n, fibonacci(n) + k - 1, 0); \\ Andrew Howroyd, Aug 10 2018

Extensions

Name changed and terms a(56) and beyond from Andrew Howroyd, Aug 10 2018