A300154 Consider a spiral on an infinite hexagonal grid. a(n) is the number of cells in the part of the spiral from 1st to n-th cell that are on the same column or diagonal (in any of three directions) as the n-th cell along the spiral, including that cell itself.

1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 6, 7, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 11, 9, 10, 11, 10, 11, 12, 10, 11, 12, 13, 11, 12, 13, 11, 12, 13, 14, 12, 13, 14, 15, 12, 13, 14, 15, 13, 14, 15, 16, 13, 14, 15, 16, 17, 14

Offset

1,2

Comments

A138099 and A280026 are analogs for the square grid. - Andrey Zabolotskiy, Mar 05 2018

Links

Peter Kagey, Table of n, a(n) for n = 1..5000

Code Golf Stack Exchange, What can you see on a hexagonal spiral?

Emily Chitwood, Example of cell sight

Emily Chitwood, Example of spiral path

Emily Chitwood, Example of initial terms

Peter Kagey, An animated illustration of the first fifteen terms.

Example

a(3) = 3 because the third hexagon is on the same diagonal as itself, the second hexagon, and the original hexagon.
a(7) = 5 because the 7th cell is on the same columns/diagonals as cells No. 2 (in one direction), 6 (in another direction), 1 and 4 (in the third direction), plus itself.

Crossrefs

Sequence in context: A000267 A249728 A060020 * A166127 A143502 A070984

Adjacent sequences: A300151 A300152 A300153 * A300155 A300156 A300157

Keyword

nonn,easy

Author

Emily Chitwood and Kimberly Johnsen, Feb 26 2018

Status

approved