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Triangle, A097806 * A127647, read by rows.
3

%I #9 Feb 18 2022 22:21:08

%S 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 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 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 Triangle, A097806 * A127647, read by rows.

%C Row sums = A000045 starting (1, 2, 3, 5, 8, 13, ...). A128540 = A127647 * A097806.

%H G. C. Greubel, <a href="/A128541/b128541.txt">Rows n = 0..100 of triangle, flattened</a>

%F A097806 * A127647 as infinite lower triangular matrices.

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 0, 1, 2;

%e 0, 0, 2, 3;

%e 0, 0, 0, 3, 5;

%e 0, 0, 0, 0, 5, 8;

%e ...

%t 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 (PARI) T(n,k) = if(k==n, fibonacci(n+1), if(k==n-1, fibonacci(n), 0)); \\ _G. C. Greubel_, Jul 11 2019

%o (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 (Sage)

%o def T(n, k):

%o if (k==n): return fibonacci(n+1)

%o elif (k==n-1): return fibonacci(n)

%o else: return 0

%o [[T(n, k) for k in (0..n)] for n in (0..15)] # _G. C. Greubel_, Jul 11 2019

%Y Cf. A000045, A097806, A127647, A128540.

%K nonn,tabl

%O 0,6

%A _Gary W. Adamson_, Mar 10 2007

%E More terms added by _G. C. Greubel_, Jul 11 2019