A214985 - OEIS

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A214985

Array: T(m,n) = (F(n) + F(2*n) + ... + F(n*m))/F(n), by antidiagonals; transpose of A214984.

2

1, 1, 2, 1, 4, 4, 1, 5, 12, 7, 1, 8, 22, 33, 12, 1, 12, 56, 94, 88, 20, 1, 19, 134, 385, 399, 232, 33, 1, 30, 342, 1487, 2640, 1691, 609, 54, 1, 48, 872, 6138, 16492, 18096, 7164, 1596, 88, 1, 77, 2256, 25319, 110143, 182900, 124033, 30348, 4180, 143

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

row 1: A001612 (except for initial term)

col 1: A000071

col 2: A027941

col 3: A049652

col 4: A092521

col 6: A049664

col 8: A156093 without minus signs

LINKS

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

FORMULA

For odd-numbered columns (m odd):

T(m,n) = (F(m*n+m) + F(m*n) - F(m))/(F(m)*L(m)).

For even-numbered columns (m even):

T(m,n) = (F(m*n+m) - F(m*n) - F(m))/(F(m)*(L(m)-1)).

EXAMPLE

Northwest corner:

1....1.....1......1.......1

2....4.....5......8.......12

4....12....22.....56......134

7....33....94.....385.....1487

12...88....399....2640....16492

20...232...1691...18096...182900

MATHEMATICA

F[n_] := Fibonacci[n]; L[n_] := LucasL[n];

t[m_, n_] := (1/F[n])*Sum[F[k*n], {k, 1, m}]

TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]

Flatten[Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}]]

CROSSREFS

Cf. A214978, A214984, A214986.

Sequence in context: A137593 A009949 A070785 * A105537 A115237 A105542

Adjacent sequences: A214982 A214983 A214984 * A214986 A214987 A214988

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Oct 28 2012

STATUS

approved