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A214978 Array T(m,n) = Fibonacci(m*n)/Fibonacci(m), by antidiagonals; transpose of A028412.

%I A214978 #21 Oct 27 2024 20:29:33
%S A214978 1,1,1,2,3,1,3,8,4,1,5,21,17,7,1,8,55,72,48,11,1,13,144,305,329,122,
%T A214978 18,1,21,377,1292,2255,1353,323,29,1,34,987,5473,15456,15005,5796,842,
%U A214978 47,1,55,2584,23184,105937,166408,104005,24447,2208,76,1,89
%N A214978 Array T(m,n) = Fibonacci(m*n)/Fibonacci(m), by antidiagonals; transpose of A028412.
%C A214978 The main entry is the transpose, A028412.  In the present format, the array can be compared directly with A214984 and A214986.
%H A214978 Clark Kimberling, <a href="/A214978/b214978.txt">Antidiagonals n = 1..60, flattened</a>
%F A214978 T(m,n) = Fibonacci(m*n)/Fibonacci(m).
%e A214978 Northwest corner:
%e A214978   1  1   2    3      5       8
%e A214978   1  3   8   21     55     144
%e A214978   1  4  17   72    305    1292
%e A214978   1  7  48  329   2255   15456
%e A214978   1 11 122 1353  15005  166408
%e A214978   1 18 323 5796 104005 1866294
%t A214978 F[n_] := Fibonacci[n]; t[m_, n_] := F[m*n]/F[m]
%t A214978 TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]
%t A214978 u = Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}];
%t A214978 v[n_] := Sum[F[m*(n + 1 - m)]/F[m], {m, 1, n}];
%t A214978 Flatten[u]                           (* A213978 *)
%t A214978 Flatten[Table[t[n, n], {n, 1, 20}]]  (* A051294 *)
%t A214978 Table[(t[n, 5] - 5)/50, {n, 1, 20}]  (* A214982 *)
%t A214978 Table[v[n], {n, 1, 30}]              (* A214983 *)
%Y A214978 Cf. A000045, A028412, A214982, A214983, A214984, A214986.
%K A214978 nonn,tabl
%O A214978 1,4
%A A214978 _Clark Kimberling_, Oct 27 2012