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%I #17 Feb 17 2018 20:02:13
%S 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 18,1,21,377,1292,2255,1353,323,29,1,34,987,5473,15456,15005,5796,842,
%U 47,1,55,2584,23184,105937,166408,104005,24447,2208,76,1,89
%N Array T(m,n) = Fibonacci(m*n)/Fibonacci(m), by antidiagonals; transpose of A028412.
%C The main entry is the transpose, A028412. In the present format, the array can be compared directly with A214984 and A214986.
%H Clark Kimberling, <a href="/A214978/b214978.txt">Antidiagonals n = 1..60, flattened</a>
%F T[(m,n) = Fibonacci(m*n)/Fibonacci(m).
%e Northwest corner:
%e 1 1 2 3 5 8
%e 1 3 8 21 55 144
%e 1 4 17 72 305 1292
%e 1 7 48 329 2255 15456
%e 1 11 122 1353 15005 166408
%e 1 18 323 5796 104005 1866294
%t F[n_] := Fibonacci[n]; t[m_, n_] := F[m*n]/F[m]
%t TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]
%t u = Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}];
%t v[n_] := Sum[F[m*(n + 1 - m)]/F[m], {m, 1, n}];
%t Flatten[u] (* A213978 *)
%t Flatten[Table[t[n, n], {n, 1, 20}]] (* A051294 *)
%t Table[(t[n, 5] - 5)/50, {n, 1, 20}] (* A214982 *)
%t Table[v[n], {n, 1, 30}] (* A214983 *)
%Y Cf. A000045, A028412, A214982, A214983, A214984, A214986.
%K nonn,tabl
%O 1,4
%A _Clark Kimberling_, Oct 27 2012
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