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

Author

Clark Kimberling, Oct 27 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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