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A373584
a(n) is equal to the number of shaded cells in a regular hexagon with side n drawn on a hexagonal grid.
1
1, 7, 13, 19, 31, 49, 67, 85, 109, 139, 169, 199, 235, 277, 319, 361, 409, 463, 517, 571, 631, 697, 763, 829, 901, 979, 1057, 1135, 1219, 1309, 1399, 1489, 1585, 1687, 1789, 1891, 1999, 2113, 2227, 2341, 2461, 2587, 2713, 2839, 2971, 3109, 3247, 3385, 3529
OFFSET
1,2
COMMENTS
On a hexagonal grid, cells are colored as follows: one cell and all those located along three straight lines passing through the center of the original cell and forming six 60° angles between each other are painted. In each of these corners, cells are painted over so that a V-shaped arrangement of cells repeats ad infinitum. The number of shaded cells in regular hexagons centered on the starting cell determines the sequence a(n).
FORMULA
a(n+4) = a(n) + 12*n + 18.
a(n) = 6*ceiling(n*(n - 1)/4) + 1.
a(n) = A003215(n) - 6*A011848(n+1).
a(n) = 6*A054925(n) + 1.
G.f.: (1 + 4*x - 4*x^2 + 4*x^3 + x^4)/((1 - x)^3*(1 + x^2)). - Stefano Spezia, Jun 11 2024
EXAMPLE
a(3) = 19 - 6*1 = 13;
a(4) = 37 - 6*3 = 19.
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1 7 13 19 31
MATHEMATICA
Table[6*Ceiling[n*(n - 1)/4] + 1, {n, 100}] (* Paolo Xausa, Jul 01 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nicolay Avilov, Jun 10 2024
STATUS
approved