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 A275113 a(n) is the minimal number of squares needed to enclose n squares with a wall so that there is a gap of at least one cell between the wall and the enclosed cells. 1
 12, 14, 15, 16, 16, 17, 18, 18, 19, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Inspired by beehive construction in which wax is used in the most efficient way. This problem is likened to construction of a fence around a house with minimum materials and maximum enclosed area. I conjectured that a specific house pattern shall be selected. See illustration in links. If the conjecture in A261491 is true (i.e., A261491(n) is the number of squares required to enclose n squares without a gap), then a(n) = A261491(n) + 8. - Charlie Neder, Jul 11 2018 LINKS Kival Ngaokrajang, Illustration of initial terms EXAMPLE a(1) = 12:      +--+--+--+      | 1| 2| 3|   +--+--+--+--+--+   |12|        | 4|   +--+  +--+  +--+   |11|  | 1|  | 5|   +--+  +--+  +--+   |10|        | 6|   +--+--+--+--+--+      | 9| 8| 7|      +--+--+--+ .       a(2) = 14:      +--+--+--+--+      | 1| 2| 3| 4|   +--+--+--+--+--+--+   |14|           | 5|   +--+  +--+--+  +--+   |13|  | 1| 2|  | 6|   +--+  +--+--+  +--+   |12|           | 7|   +--+--+--+--+--+--+      |11|10| 9| 8|      +--+--+--+--+ .      a(3) = 15:      +--+--+--+      | 1| 2| 3|   +--+--+--+--+--+   |15|        | 4|   +--+  +--+  +--+--+   |14|  | 3|     | 5|   +--+  +--+--+  +--+   |13|  | 1| 2|  | 6|   +--+  +--+--+  +--+   |12|           | 7|   +--+--+--+--+--+--+      |11|10| 9| 8|      +--+--+--+--+ CROSSREFS Cf. A235382, A261491. Sequence in context: A075477 A075482 A248019 * A043651 A043701 A290001 Adjacent sequences:  A275110 A275111 A275112 * A275114 A275115 A275116 KEYWORD nonn,more AUTHOR Kival Ngaokrajang, Jul 17 2016 STATUS approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)