A128541 Triangle, A097806 * A127647, read by rows.

1, 1, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 5, 0, 0, 0, 0, 5, 8, 0, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 13, 21, 0, 0, 0, 0, 0, 0, 0, 21, 34, 0, 0, 0, 0, 0, 0, 0, 0, 34, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 233

Offset

0,6

Comments

Row sums = A000045 starting (1, 2, 3, 5, 8, 13, ...). A128540 = A127647 * A097806.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

A097806 * A127647 as infinite lower triangular matrices.

Example

First few rows of the triangle:
  1;
  1, 1;
  0, 1, 2;
  0, 0, 2, 3;
  0, 0, 0, 3, 5;
  0, 0, 0, 0, 5, 8;
  ...

Mathematica

Table[If[k==n, Fibonacci[n+1], If[k==n-1, Fibonacci[n], 0]], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 11 2019 *)

Prog

(PARI) T(n, k) = if(k==n, fibonacci(n+1), if(k==n-1, fibonacci(n), 0)); \\ G. C. Greubel, Jul 11 2019
(Magma) [k eq n select Fibonacci(n+1) else k eq n-1 select Fibonacci(n) else 0: k in [0..n], n in [0..15]]; // G. C. Greubel, Jul 11 2019
(Sage)
def T(n, k):
    if (k==n): return fibonacci(n+1)
    elif (k==n-1): return fibonacci(n)
    else: return 0
[[T(n, k) for k in (0..n)] for n in (0..15)] # G. C. Greubel, Jul 11 2019

Crossrefs

Cf. A000045, A097806, A127647, A128540.

Sequence in context: A282133 A338819 A153869 * A122908 A296441 A091008

Adjacent sequences: A128538 A128539 A128540 * A128542 A128543 A128544

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 10 2007

Extensions

More terms added by G. C. Greubel, Jul 11 2019

Status

approved