A211782 Rectangular array: R(n,k)=[n/F(2)]+[n/F(3)]+...+[n/F(k+1)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.

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

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 begins with 1,3,5,7,9,12,13,16,18,21,22,25.

Links

Table of n, a(n) for n=1..84.

Example

Northwest corner:
1...2...3...4...5...6....7....8
1...3...4...6...7...9....10...12
1...3...5...7...8...11...12...14
1...3...5...7...9...12...13...15
1...3...5...7...9...12...13...16

Mathematica

f[n_, m_] := Sum[Floor[n/Fibonacci[k + 1]], {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. A000045, A211701.

Sequence in context: A263916 A210258 A181108 * A211701 A183110 A117895

Adjacent sequences: A211779 A211780 A211781 * A211783 A211784 A211785

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 20 2012

Status

approved