A132921 Triangle read by rows: T(n,k) = n + Fibonacci(k) - 1, 1 <= k <= n.

1, 2, 2, 3, 3, 4, 4, 4, 5, 6, 5, 5, 6, 7, 9, 6, 6, 7, 8, 10, 13, 7, 7, 8, 9, 11, 14, 19, 8, 8, 9, 10, 12, 15, 20, 28, 9, 9, 10, 11, 13, 16, 21, 29, 42, 10, 10, 11, 12, 14, 17, 22, 30, 43, 64, 11, 11, 12, 13, 15, 18, 23, 31, 44, 65, 99, 12, 12, 13, 14, 16, 19, 24, 32, 45, 66, 100, 155

Offset: 1

Author

Gary W. Adamson, Sep 05 2007

Keywords

• nonn
• tabl

Comments

Right border = A081659, row sums = A132922: (1, 4, 10, 19, 32, ...).

Examples

			First few rows of the triangle are:
  1;
  2, 2;
  3, 3, 4;
  4, 4, 5, 6;
  5, 5, 6, 7, 9;
  ...
Column 3 = 4, 5, 6, 7, ...; since A081659(2) = 4.
		

Links

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

Crossrefs

Row sums are A132922.

Cf. A127648, A127647, A081659.

Programs

Mathematica

T[n_,k_]:=n+Fibonacci[k]-1;Table[T[n,k],{n,12},{k,n}]//Flatten (* James C. McMahon, Mar 09 2025 *)

PARI

T(n,k)=if(k<=n, n + fibonacci(k) - 1, 0) \\ Andrew Howroyd, Sep 01 2018

Formula

Equals (A127648 * A000012 + A000012 * A127647) - A000012 as infinite lower triangular matrices.

Extensions

Name clarified and terms a(56) and beyond from Andrew Howroyd, Sep 01 2018