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A214978 Array T(m,n) = Fibonacci(m*n)/Fibonacci(m), by antidiagonals; transpose of A028412. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 11:23 EDT 2021. Contains 347556 sequences. (Running on oeis4.)