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

Author

Gary W. Adamson, Mar 10 2007

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
  ...
		

Links

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

Crossrefs

Cf. A000045, A097806, A127647, A128540.

Programs

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

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 *)

PARI

T(n,k) = if(k==n, fibonacci(n+1), if(k==n-1, fibonacci(n), 0)); \\ 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

Formula

A097806 * A127647 as infinite lower triangular matrices.

Extensions

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