%I #19 Sep 08 2022 08:45:29

%S 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,

%T 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,

%U 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

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

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

%C 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

%H G. C. Greubel, <a href="/A127647/b127647.txt">Rows n = 1..100 of triangle, flattened</a>

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

%F G.f.: -x*y/(-1+x*y+x^2*y^2). - _R. J. Mathar_, Aug 11 2015

%e First few rows of the triangle:

%e 1;

%e 0, 1;

%e 0, 0, 2;

%e 0, 0, 0, 3;

%e 0, 0, 0, 0, 5;

%e 0, 0, 0, 0, 0, 8;

%t Flatten[Table[{Table[0,{n-1}],Fibonacci[n]},{n,15}]] (* _Harvey P. Dale_, Jan 11 2016 *)

%o (PARI) T(n,k)=if(k==n, fibonacci(n), 0); \\ _G. C. Greubel_, Jul 11 2019

%o (Magma) [k eq n select Fibonacci(n) else 0: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Jul 11 2019

%o (Sage)

%o def T(n, k):

%o if (k==n): return fibonacci(n)

%o else: return 0

%o [[T(n, k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Jul 11 2019

%Y Cf. A007318, A094436, A016095.

%K nonn,tabl,easy

%O 1,6

%A _Gary W. Adamson_, Jan 22 2007