A361400 a(n) is the product of n and the number displayed on the upper face of a six-sided die as a result of its rotation through the edge when rolling over the cell with the number n of the square spiral of the natural row.

1, 4, 9, 4, 20, 12, 21, 8, 36, 60, 22, 12, 65, 56, 30, 48, 85, 18, 38, 120, 105, 66, 46, 96, 125, 78, 162, 112, 29, 90, 186, 160, 33, 68, 210, 180, 37, 114, 234, 160, 41, 126, 258, 220, 45, 92, 282, 240, 49, 100, 153, 260, 212, 108, 165, 280, 228, 58, 177, 360, 244

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

Table of n, a(n) for n=1..61.

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

Cf. A361136.

Sequence in context: A131016 A204996 A061369 * A291645 A340769 A088377

Adjacent sequences: A361397 A361398 A361399 * A361401 A361402 A361403

Keyword

nonn

Author

Nicolay Avilov, Mar 10 2023

Status

approved