

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



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
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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: A194331 A290600 A143595 * A208521 A209570 A205703
Adjacent sequences: A211699 A211700 A211701 * A211703 A211704 A211705


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Apr 19 2012


STATUS

approved



