cp's OEIS Frontend

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.

%I A341160 #16 Feb 12 2021 11:37:48
%S A341160 1,28,180,622,1910,3880,8162,17592,28600,45380,79376,122592,174889,
%T A341160 223556,313350,393912,604421,792202,1089859,1410896,1644223,2120976,
%U A341160 2923991,3369408,4002500,5136496,6298670,7476224,8323935,9464220,10653646,12985600,17233062,20321768,22053045,27665722
%N 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.
%C A341160 See A341327 for the list of the spiral numbers not covered by any square in the tiling.
%H A341160 Scott R. Shannon, <a href="/A341160/a341160.png">Image of the first 60 squares</a>. 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.
%e A341160 The square spiral used is:
%e A341160 .
%e A341160   17--16--15--14--13   .
%e A341160    |               |   .
%e A341160   18   5---4---3  12   29
%e A341160    |   |       |   |   |
%e A341160   19   6   1---2  11   28
%e A341160    |   |           |   |
%e A341160   20   7---8---9--10   27
%e A341160    |                   |
%e A341160   21--22--23--24--25--26
%e A341160 .
%e A341160 a(1) = 1 as a square of size 1 x 1 is placed on the number 1, which is the minimum possible value.
%e A341160 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.
%e A341160 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.
%Y A341160 Cf. A341327 (spiral numbers not covered), A340974 (lines), A174344, A274923, A296030, A275161.
%K A341160 nonn
%O A341160 1,2
%A A341160 _Scott R. Shannon_, Feb 06 2021