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A128541 Triangle, A097806 * A127647, read by rows.

%I A128541 #9 Feb 18 2022 22:21:08
%S A128541 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,
%T A128541 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,
%U A128541 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
%N A128541 Triangle, A097806 * A127647, read by rows.
%C A128541 Row sums = A000045 starting (1, 2, 3, 5, 8, 13, ...). A128540 = A127647 * A097806.
%H A128541 G. C. Greubel, <a href="/A128541/b128541.txt">Rows n = 0..100 of triangle, flattened</a>
%F A128541 A097806 * A127647 as infinite lower triangular matrices.
%e A128541 First few rows of the triangle:
%e A128541   1;
%e A128541   1, 1;
%e A128541   0, 1, 2;
%e A128541   0, 0, 2, 3;
%e A128541   0, 0, 0, 3, 5;
%e A128541   0, 0, 0, 0, 5, 8;
%e A128541   ...
%t A128541 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 *)
%o A128541 (PARI) T(n,k) = if(k==n, fibonacci(n+1), if(k==n-1, fibonacci(n), 0)); \\ _G. C. Greubel_, Jul 11 2019
%o A128541 (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
%o A128541 (Sage)
%o A128541 def T(n, k):
%o A128541     if (k==n): return fibonacci(n+1)
%o A128541     elif (k==n-1): return fibonacci(n)
%o A128541     else: return 0
%o A128541 [[T(n, k) for k in (0..n)] for n in (0..15)] # _G. C. Greubel_, Jul 11 2019
%Y A128541 Cf. A000045, A097806, A127647, A128540.
%K A128541 nonn,tabl
%O A128541 0,6
%A A128541 _Gary W. Adamson_, Mar 10 2007
%E A128541 More terms added by _G. C. Greubel_, Jul 11 2019