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

Author

Clark Kimberling, Apr 19 2012

Keywords

• nonn
• tabl

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.

Examples

			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
		

Crossrefs

Cf. A211701.

Programs

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}]]