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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.

%I A300154 #37 Mar 19 2020 02:21:17
%S A300154 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,
%T A300154 11,12,10,11,12,13,11,12,13,11,12,13,14,12,13,14,15,12,13,14,15,13,14,
%U A300154 15,16,13,14,15,16,17,14
%N 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.
%C A300154 A138099 and A280026 are analogs for the square grid. - _Andrey Zabolotskiy_, Mar 05 2018
%H A300154 Peter Kagey, <a href="/A300154/b300154.txt">Table of n, a(n) for n = 1..5000</a>
%H A300154 Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/201259/53884">What can you see on a hexagonal spiral?</a>
%H A300154 Emily Chitwood, <a href="/A300154/a300154_3.jpg">Example of cell sight</a>
%H A300154 Emily Chitwood, <a href="/A300154/a300154_4.jpg">Example of spiral path</a>
%H A300154 Emily Chitwood, <a href="/A300154/a300154_5.jpg">Example of initial terms</a>
%H A300154 Peter Kagey, <a href="/A300154/a300154.gif">An animated illustration of the first fifteen terms</a>.
%e A300154 a(3) = 3 because the third hexagon is on the same diagonal as itself, the second hexagon, and the original hexagon.
%e A300154 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.
%K A300154 nonn,easy
%O A300154 1,2
%A A300154 _Emily Chitwood_ and _Kimberly Johnsen_, Feb 26 2018