A294249 Minimum number of matchsticks required to make squares of size 1 X 1, 2 X 2, ..., n X n simultaneously.

0, 4, 10, 17, 26, 35, 45, 56, 69, 82, 95, 109, 125, 140, 156, 172, 190, 208, 226, 243, 264, 282, 300, 322, 340, 363, 388, 409, 435, 454, 480, 504, 528, 553, 581, 603, 629, 659, 684, 713, 740, 765, 795, 822, 843, 880, 909

Offset

0,2

Comments

Problem originally suggested by and first terms computed by Robert P. Vermillion Jr.

These are the result of computer searches, and while all efforts have been made to ensure that they are in fact the minimum, some chance remains that smaller values may be found.

Upper bounds for a(47)-a(63) are 939, 968, 999, 1030, 1061, 1093, 1122, 1157, 1186, 1217, 1250, 1281, 1311, 1350, 1383, 1417, 1451. - Benjamin Chaffin, Aug 03 2018

Links

Table of n, a(n) for n=0..46.

Benjamin Chaffin, Optimal solutions up to n=46, and best known up to n=63

Benjamin Chaffin, Matchstick Squares.

Example

Illustration for a(2) = 10 from N. J. A. Sloane, Oct 30 2017
o - o - o
|   |   |
o - o   o
|       |
o - o - o

Crossrefs

Sequence in context: A301288 A347154 A009860 * A138105 A389316 A213398

Adjacent sequences: A294246 A294247 A294248 * A294250 A294251 A294252

Keyword

nonn,more

Author

Colin D Wright, Oct 26 2017

Extensions

Confirmed a(0)-a(29) and extended to a(46) by Benjamin Chaffin, Aug 03 2018

Status

approved