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

%I A127647 #19 Sep 08 2022 08:45:29
%S A127647 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 A127647 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 A127647 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 A127647 Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).
%C A127647 This sequence * A007318 (Pascal's Triangle) = A016095. A007318 * this sequence = A094436
%C A127647 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 A127647 G. C. Greubel, <a href="/A127647/b127647.txt">Rows n = 1..100 of triangle, flattened</a>
%F A127647 An infinite lower triangular matrix with the Fibonacci sequence in the main diagonal and the rest zeros.
%F A127647 G.f.: -x*y/(-1+x*y+x^2*y^2). - _R. J. Mathar_, Aug 11 2015
%e A127647 First few rows of the triangle:
%e A127647   1;
%e A127647   0, 1;
%e A127647   0, 0, 2;
%e A127647   0, 0, 0, 3;
%e A127647   0, 0, 0, 0, 5;
%e A127647   0, 0, 0, 0, 0, 8;
%t A127647 Flatten[Table[{Table[0,{n-1}],Fibonacci[n]},{n,15}]] (* _Harvey P. Dale_, Jan 11 2016 *)
%o A127647 (PARI) T(n,k)=if(k==n, fibonacci(n), 0); \\ _G. C. Greubel_, Jul 11 2019
%o A127647 (Magma) [k eq n select Fibonacci(n) else 0: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Jul 11 2019
%o A127647 (Sage)
%o A127647 def T(n, k):
%o A127647     if (k==n): return fibonacci(n)
%o A127647     else: return 0
%o A127647 [[T(n, k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Jul 11 2019
%Y A127647 Cf. A007318, A094436, A016095.
%K A127647 nonn,tabl,easy
%O A127647 1,6
%A A127647 _Gary W. Adamson_, Jan 22 2007