A390524 - OEIS

%I #11 Nov 13 2025 20:16:20

%S 0,0,0,0,1,0,0,1,2,0,0,2,2,3,0,0,3,4,3,4,0,0,5,6,6,4,5,0,0,8,10,9,8,5,

%T 6,0,0,13,16,15,12,10,6,7,0,0,21,26,24,20,15,12,7,8,0,0,34,42,39,32,

%U 25,18,14,8,9,0,0,55,68,63,52,40,30,21,16,9,10,0

%N Array read by ascending antidiagonals: A(n, k) = k * Fibonacci(n).

%F G.f.: x*y/((1 - x - x^2)*(1 - y)^2).

%F E.g.f.: 2*exp(x/2+y)*y*sinh(sqrt(5)*x/2)/sqrt(5).

%F Sum_{k=0..n} A(n, k) = A001924(n-1).

%e The array begins as:

%e   0, 0,  0,  0,  0,  0,  0, ...

%e   0, 1,  2,  3,  4,  5,  6, ...

%e   0, 1,  2,  3,  4,  5,  6, ...

%e   0, 2,  4,  6,  8, 10, 12, ...

%e   0, 3,  6,  9, 12, 15, 18, ...

%e   0, 5, 10, 15, 20, 25, 30, ...

%e   ...

%t A[n_,k_]:=k*Fibonacci[n]; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten

%Y Cf. A001924, A045925 (main diagonal).

%Y Columns give: A000004 (k=0), A000045 (k=1), A022086 - A022093 (k=3..9), A022345 - A022366 (k=11..32).

%Y Rows give: A000004 (n=0), A001477 (n=1..2), A005843 (n=3), A008585 (n=4), A008587 (n=5), A008590 (n=6).

%K nonn,easy,tabl

%O 0,9

%A _Stefano Spezia_, Nov 09 2025