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A299965
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Number of triangles in a Star of David of size n.
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3
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0, 20, 118, 348, 764, 1420, 2370, 3668, 5368, 7524, 10190, 13420, 17268, 21788, 27034, 33060, 39920, 47668, 56358, 66044, 76780, 88620, 101618, 115828, 131304, 148100, 166270, 185868, 206948, 229564, 253770, 279620, 307168, 336468, 367574, 400540, 435420, 472268
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OFFSET
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0,2
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COMMENTS
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In a Star of David of size n, there are A135453(n) "size=1" triangles and 2*A228887(n) "size>1" triangles. See formula.
The number of matchstick units is A045946.
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LINKS
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FORMULA
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a(n) = 9*n^3 + 12*n^2 - n.
G.f.: 2*x*(10 - x)*(1 + 2*x) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.
(End)
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EXAMPLE
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For n=1, there are 12 (size=1) + 6 (size=4) + 2 (size=9) = 20 triangles.
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PROG
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(PARI) concat(0, Vec(2*x*(10 - x)*(1 + 2*x) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Apr 04 2019
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CROSSREFS
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For the total number of triangles in a different arrangement, see A002717 (for triangular matchstick), A045949 (for hexagonal matchstick).
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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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