A127647 Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).

1, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 233, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 377

Offset: 1

Author

Gary W. Adamson, Jan 22 2007

Keywords

• nonn
• tabl
• easy

Comments

This sequence * A007318 (Pascal's Triangle) = A016095. A007318 * this sequence = A094436

With offset (0,6), this is [0,0,0,0,0,0,0,0,0,0,...] DELTA [1,1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 26 2007

Examples

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

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A007318, A094436, A016095.

Programs

Magma

[k eq n select Fibonacci(n) else 0: k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 11 2019

Mathematica

Flatten[Table[{Table[0,{n-1}],Fibonacci[n]},{n,15}]] (* Harvey P. Dale, Jan 11 2016 *)

PARI

T(n,k)=if(k==n, fibonacci(n), 0); \\ G. C. Greubel, Jul 11 2019

Sage

def T(n, k):
    if (k==n): return fibonacci(n)
    else: return 0
[[T(n, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Jul 11 2019

Formula

An infinite lower triangular matrix with the Fibonacci sequence in the main diagonal and the rest zeros.

G.f.: -x*y/(-1+x*y+x^2*y^2). - R. J. Mathar, Aug 11 2015