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A127647 Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n). 17
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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

LINKS

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

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

EXAMPLE

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;

MATHEMATICA

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

PROG

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

(MAGMA) [k eq n select Fibonacci(n) else 0: k in [1..n], n in [1..15]]; // 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

CROSSREFS

Cf. A007318, A094436, A016095.

Sequence in context: A218272 A134402 A174712 * A325458 A226728 A244140

Adjacent sequences:  A127644 A127645 A127646 * A127648 A127649 A127650

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jan 22 2007

STATUS

approved

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Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)