A341160 The sum of the numbers inside the squares of incrementing size n x n when the square spiral is tiled with these squares, where each tile contains numbers which sum to the minimum possible value, and each number on the spiral can only be in one tile.

1, 28, 180, 622, 1910, 3880, 8162, 17592, 28600, 45380, 79376, 122592, 174889, 223556, 313350, 393912, 604421, 792202, 1089859, 1410896, 1644223, 2120976, 2923991, 3369408, 4002500, 5136496, 6298670, 7476224, 8323935, 9464220, 10653646, 12985600, 17233062, 20321768, 22053045, 27665722

Offset: 1

Author

Scott R. Shannon, Feb 06 2021

Keywords

• nonn

Comments

See A341327 for the list of the spiral numbers not covered by any square in the tiling.

Examples

			The square spiral used is:
.
  17--16--15--14--13   .
   |               |   .
  18   5---4---3  12   29
   |   |       |   |   |
  19   6   1---2  11   28
   |   |           |   |
  20   7---8---9--10   27
   |                   |
  21--22--23--24--25--26
.
a(1) = 1 as a square of size 1 x 1 is placed on the number 1, which is the minimum possible value.
a(2) = 28 as a square of size 2 x 2 is placed such that it covers the numbers 2,3,11,12 which sum to 28. This is the minimum possible sum for such a square which does not use the previously covered number 1.
a(3) = 180 as a square of size 3 x 3 is placed such that it covers numbers 4,5,18,15,16,17,34,35,36 which sum to 180. This is the minimum possible sum for such a square which does not use the previously covered numbers 1,2,3,11,12.
		

Links

• Scott R. Shannon, Image of the first 60 squares. The image can be zoomed in to see the numbers of the square spiral. The colors are graduated across the spectrum to show the squares relative size/placement order.

Crossrefs

Cf. A341327 (spiral numbers not covered), A340974 (lines), A174344, A274923, A296030, A275161.