

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.


0



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
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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 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. 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



