A214985 Array: T(m,n) = (F(n) + F(2*n) + ... + F(n*m))/F(n), by antidiagonals; transpose of A214984.

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

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