OFFSET
1,2
COMMENTS
A one-cell wide spiral is drawn along the grid lines of an infinite checkered plane, twisting clockwise (see the figure at the link). In the initial cell of the spiral is placed a die with numbers 1, 2, 3, 4, 5 and 6, in which the sum of points on opposite sides is 7, so that 1 is on its upper side, 4 is on its front and 5 is on the right. The size of the face of the cube coincides with the size of the cell of the plane. The cube, rolling over the edge, enters the next cell in a spiral, and so on, moving along the cells of the drawn spiral. The number in each cell of the spiral is multiplied by the number located on the upper face of the game cube rolling along it, and thus this sequence is obtained.
LINKS
Nicolay Avilov, Illustration for a(1) - a(4)
FORMULA
a(n) = n * A361136(n).
EXAMPLE
This is how the first 30 terms of the sequence are obtained:
.
21--22--23--24--25--26 5---3---2---4---5---3 105--66-46--96--125--78
| | | | | |
20 7---8---9--10 27 6 3---1---4---6 6 120 21--8---36--60 162
| | | | | | | | | | | |
19 6 1---2 11 28 * 2 2 1---2 2 4 = 38 12 1---4 22 112
| | | | | | | | | | | | | | |
18 5---4---3 12 29 1 4---1---3 1 1 18 20--4---9 12 29
| | | | | | | | |
17--16--15--14--13 30 5---3---2---4---5 3 85--48--30--56--65 90
.
Multiplying the corresponding numbers of the first and second spirals, we get the first 30 terms of the sequence. For example: a(10) = 10*6 = 60, a(17) = 17*5 = 85.
CROSSREFS
KEYWORD
nonn
AUTHOR
Nicolay Avilov, Mar 10 2023
STATUS
approved