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A363080
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Number of hexagonal lattice points within a hexagram centered at a lattice point and with outermost vertices at the six lattice points n steps outward from the central point.
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0
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1, 7, 13, 25, 43, 61, 85, 115, 145, 181, 223, 265, 313, 367, 421, 481, 547, 613, 685, 763, 841, 925, 1015, 1105, 1201, 1303, 1405, 1513, 1627, 1741, 1861, 1987, 2113, 2245, 2383, 2521, 2665, 2815, 2965, 3121, 3283, 3445, 3613, 3787, 3961, 4141, 4327, 4513, 4705, 4903, 5101, 5305, 5515, 5725
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OFFSET
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0,2
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COMMENTS
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In contrast, A003154 (the star numbers) counts the hexagonal lattice points within a hexagram centered at a lattice point and with the vertices of the central hexagon at the six lattice points a given number of steps outward from the central point.
Besides the first term, the first differences are given by six times A004396.
A005448 (the centered triangular numbers) counts just the lattice points within one of the two triangles that make up the hexagram.
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LINKS
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FORMULA
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a(n) = 6*ceiling(n*(n+1)/3) + 1.
a(n) = 6*A007980(n-1) + 1 for n >= 1.
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EXAMPLE
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Illustration of initial terms:
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. o o
. o o o o o
. o o o o o o o o
. o o o o o o o o o o o o o o o o
. o o o o o o o o
. o o o o o
. o o
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. 1 7 13 25
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MATHEMATICA
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Table[6*Ceiling[n*(n + 1)/3] + 1, {n, 0, 60}] (* Amiram Eldar, Jul 28 2023 *)
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PROG
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(Haskell) a(n) = 6*ceiling(n*(n+1)/3) + 1
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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