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

Author

Clark Kimberling, Oct 28 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Cf. A214978, A214984, A214986.

Programs

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}]]

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)).