A319879 a(n) = minimal number m of unit squares needed to make a figure formed from squares (joined edge to edge) which has n holes.

1, 8, 13, 18, 21, 26, 29, 34, 37, 40, 45, 48, 51, 56, 59, 62, 65, 70, 73, 76, 79, 84, 87, 90, 93, 96, 101, 104, 107, 110, 113, 118, 121, 124, 127, 130, 133, 138, 141, 144, 147, 150, 153, 158, 161, 164, 167, 170, 173, 176, 181, 184, 187, 190, 193, 196, 199, 204

Offset

0,2

Comments

The holes must not touch each other.

A valid figure needs at least one square.

References

Jean-Paul Delahaye, Des trous à entourer avec parcimonie, Pour la Science, No. 501, Juillet 2019, pp. 82-87.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

For n >= 1, a(n) = 3*(n+1) + 2*floor(sqrt(4*n-3)). - Zhuorui He, Jun 29 2026

Example

Examples from N. J. A. Sloane, Jan 30 2019 for n = 0, 1, 2, 3, 4:
  X
-----
  XXX
  XOX
  XXX
-------
  XXXXX
  XOXOX
  XXXXX
-------
  XXXXX
  XOXOX
  XXXXX
  XOX
  XXX
-------
  XXXXX
  XOXOX
  XXXXX
  XOXOX
  XXXXX

Crossrefs

Sequence in context: A014134 A085989 A389638 * A095097 A187227 A224251

Adjacent sequences: A319876 A319877 A319878 * A319880 A319881 A319882

Keyword

nonn,easy,changed

Author

Jean-Paul Delahaye, Sep 30 2018

Extensions

Entry 123 changed to 124 by the author, Jul 01 2019. - N. J. A. Sloane, Jul 01 2019

Status

approved