A211702 Rectangular array: R(n,k)=[n/F(1)]+[n/F(2)]+...+[n/F(k)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.

1, 2, 2, 3, 4, 2, 4, 6, 5, 2, 5, 8, 7, 5, 2, 6, 10, 10, 8, 5, 2, 7, 12, 12, 11, 8, 5, 2, 8, 14, 15, 13, 11, 8, 5, 2, 9, 16, 17, 17, 14, 11, 8, 5, 2, 10, 18, 20, 19, 18, 14, 11, 8, 5, 2, 11, 20, 22, 22, 20, 18, 14, 11, 8, 5, 2, 12, 22, 25, 25, 23, 20, 18, 14, 11, 8, 5, 2, 13

Offset

1,2

Comments

For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701. The sequence approached as a limit of the rows is described in the Comments section of A175346.

Links

Table of n, a(n) for n=1..79.

Example

Northwest corner:
1...2...3...4....5....6....7
2...4...6...8....10...12...15
2...5...7...10...12...15...17
2...5...8...11...13...17...19
2...5...8...11...14...18...20
2...5...8...11...14...18...20

Mathematica

f[n_, m_] := Sum[Floor[n/Fibonacci[k]], {k, 1, m}]
TableForm[Table[f[n, m], {m, 1, 20}, {n, 1, 16}]]
Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]

Crossrefs

Cf. A211701.

Sequence in context: A372606 A290600 A143595 * A208521 A209570 A205703

Adjacent sequences: A211699 A211700 A211701 * A211703 A211704 A211705

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 19 2012

Status

approved