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

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, 18, 1, 21, 377, 1292, 2255, 1353, 323, 29, 1, 34, 987, 5473, 15456, 15005, 5796, 842, 47, 1, 55, 2584, 23184, 105937, 166408, 104005, 24447, 2208, 76, 1, 89

Offset

1,4

Comments

The main entry is the transpose, A028412. In the present format, the array can be compared directly with A214984 and A214986.

Links

Clark Kimberling, Antidiagonals n = 1..60, flattened

Formula

T[(m,n) = Fibonacci(m*n)/Fibonacci(m).

Example

Northwest corner:
  1  1   2    3      5       8
  1  3   8   21     55     144
  1  4  17   72    305    1292
  1  7  48  329   2255   15456
  1 11 122 1353  15005  166408
  1 18 323 5796 104005 1866294

Mathematica

F[n_] := Fibonacci[n]; t[m_, n_] := F[m*n]/F[m]
TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]
u = Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}];
v[n_] := Sum[F[m*(n + 1 - m)]/F[m], {m, 1, n}];
Flatten[u]                           (* A213978 *)
Flatten[Table[t[n, n], {n, 1, 20}]]  (* A051294 *)
Table[(t[n, 5] - 5)/50, {n, 1, 20}]  (* A214982 *)
Table[v[n], {n, 1, 30}]              (* A214983 *)

Crossrefs

Cf. A000045, A028412, A214982, A214983, A214984, A214986.

Sequence in context: A293985 A100324 A121424 * A295380 A093768 A209419

Adjacent sequences: A214975 A214976 A214977 * A214979 A214980 A214981

Keyword

nonn,tabl

Author

Clark Kimberling, Oct 27 2012

Status

approved