A211707 Rectangular array: R(n,k)=n+[n/2+1/2]+...+[n/k+1/2], where [ ]=floor and k>=1, by antidiagonals.

1, 2, 2, 3, 3, 2, 4, 5, 4, 2, 5, 6, 6, 5, 2, 6, 8, 7, 7, 5, 2, 7, 9, 10, 8, 8, 5, 2, 8, 11, 11, 11, 9, 9, 5, 2, 9, 12, 13, 13, 12, 10, 9, 5, 2, 10, 14, 15, 15, 14, 13, 11, 9, 5, 2, 11, 15, 17, 17, 16, 15, 14, 12, 9, 5, 2, 12, 17, 18, 19, 19, 17, 16, 15, 12, 9, 5, 2, 13, 18, 21

Offset

1,2

Comments

Limit of n-th row: A056549=(2,5,9,12,17,21,25,...).

Row 1: A000027

Row 2: A007494

R(n,n)=A077024(n)

For n>=1, row n is a homogeneous linear recurrence sequence of order A005728(n) with palindromic recurrence coefficients in the sense described at A211701.

Links

Table of n, a(n) for n=1..81.

Example

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

Mathematica

f[n_, m_] := Sum[Floor[n/k + 1/2], {k, 1, m}]
TableForm[Table[f[n, m], {m, 1, 20}, {n, 1, 16}]]

Crossrefs

Cf. A211701

Sequence in context: A105496 A339575 A167618 * A303363 A045796 A127684

Adjacent sequences: A211704 A211705 A211706 * A211708 A211709 A211710

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 20 2012

Status

approved