A193588 A Fibonacci triangle: T(n,k) = Fib(k+2) for 0 <= k <= n.

1, 1, 2, 1, 2, 3, 1, 2, 3, 5, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 13, 1, 2, 3, 5, 8, 13, 21, 1, 2, 3, 5, 8, 13, 21, 34, 1, 2, 3, 5, 8, 13, 21, 34, 55, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

Offset

0,3

Comments

n-th row sum: A001911, Fib(n+3)-2;

n-th alternating row sum: A000045, F(n).

The augmentation (as defined at A193091) of A193588 is A193589.

Links

Table of n, a(n) for n=0..77.

Formula

a(n) = A115346(n) + 1. - Filip Zaludek, Nov 19 2016

Example

First 5 rows of A193588:
  1;
  1, 2;
  1, 2, 3;
  1, 2, 3, 5;
  1, 2, 3, 5, 8;

Mathematica

(See A193589, the augmentation of A193588.)
Table[Fibonacci[k+2], {n, 0, 20}, {k, 0, n}]//Flatten (* Harvey P. Dale, Nov 29 2017 *)
Module[{nn=15, fibs}, fibs=Fibonacci[Range[2, nn]]; Table[Take[fibs, n], {n, nn-1}]]// Flatten (* Harvey P. Dale, Mar 02 2023 *)

Crossrefs

Cf. A193588.

Sequence in context: A060040 A092080 A264482 * A165884 A263939 A347499

Adjacent sequences: A193585 A193586 A193587 * A193589 A193590 A193591

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 31 2011

Status

approved