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%I #28 Jan 10 2021 22:25:29
%S 1,17,33,46
%N Solution to stacking stones puzzle (see Comments).
%C This is a variant of the stepping stone puzzle sequence (A337663), where you start by placing n 1's on an infinite square grid. Then place the numbers 2,3,... in order on the grid, following the rule that the sum of the 8 surrounding cells has to be equal to the number placed on a cell. a(n) is the largest number which can be achieved starting with n 1's. Additionally, there are 2 different new rules in this "stacking stones" sequence:
%C 1. You can "stack" numbers on top of already placed numbers when the sum of the surrounding 8 cells is equal to the new number. The number inside the cell is not added to the sum and is replaced as value of the cell with the new number.
%C 2. The starting 1's have to be at least one cell apart (to avoid a trivial infinite solution).
%H S. Brunner, <a href="/A340000/a340000.txt">Python program</a>
%e Illustration for a(3)=33:
%e +------+------+------+------+------+------+------+
%e | | | | | | | |
%e | | | 18 | 17 | 26 | | 33 |
%e | | | | [4] | [13] | | |
%e +------+------+------+------+------+------+------+
%e | | | | | | | |
%e | | | | 1 | 3 | 5 | 28 |
%e | | | | | | | |
%e +------+------+------+------+------+------+------+
%e | | | | | | | |
%e | | 21 | 14 | 27 | 2 | 23 | |
%e | | | | [6] | | [11] | |
%e +------+------+------+------+------+------+------+
%e | | | | | | | |
%e | 22 | | 7 | | | 1 | 24 |
%e | | | | | | | [12] |
%e +------+------+------+------+------+------+------+
%e | | | | | | | |
%e | | 1 | 8 | 31 | 32 | | 25 |
%e | | | | [15] | [16] | | |
%e +------+------+------+------+------+------+------+
%e | 30 | 29 | | | | | |
%e | [20] | [19] | | | | | |
%e | [10] | [9] | | | | | |
%e +------+------+------+------+------+------+------+
%e Illustration for a(4)=46:
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | | | | |
%e | 32 | | 37 | 44 | | | | | | | | |
%e | | | [15] | [22] | | | | | | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | | | | |
%e | 24 | 8 | 7 | | | 39 | | | | 42 | | 29 |
%e | | | | | | | | | | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | 31 | | | | | | | | |
%e | | 16 | 1 | [13] | 18 | 21 | | | | 41 | 1 | 28 |
%e | | | | [6] | | | | | | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | | | | |
%e | | 17 | | 2 | 3 | | | 43 | | 40 | | 27 |
%e | | | | | | | | | | [14] | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | | | | |
%e | | 36 | 19 | | 34 | 4 | 9 | 33 | 1 | 12 | 26 | |
%e | | | | | [1] | | | [10] | | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | 46 | | | |
%e | | | | 20 | | 5 | | | [23] | | 38 | |
%e | | | | | | | | | [11] | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%e | | | | | | | | | | | | |
%e | | | | 45 | 25 | 30 | 35 | | | | | |
%e | | | | | | | | | | | | |
%e +------+------+------+------+------+------+------+------+------+------+------+------+
%Y Cf. A337663.
%K nonn,more,hard
%O 1,2
%A _S. Brunner_, Dec 26 2020
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