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A270700
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Triangular Star of David numbers (the figurate number of triangles framing a hexagram: a(0) = 12; thereafter a(n) = 36*n+6).
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3
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12, 42, 78, 114, 150, 186, 222, 258, 294, 330, 366, 402, 438, 474, 510, 546, 582, 618, 654, 690, 726, 762, 798, 834, 870, 906, 942, 978, 1014, 1050, 1086, 1122, 1158, 1194, 1230, 1266, 1302, 1338, 1374, 1410, 1446, 1482, 1518, 1554, 1590, 1626, 1662, 1698, 1734
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OFFSET
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0,1
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COMMENTS
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Also known as unitary triangular hexagram numbers, according to the author.
After a(0), the sum of inner and outer perimeters of triangle edges forming each hexagram is [36n - 6], always 12 less than the number of triangles framing the hexagram. Where a(0)=12, the perimeter is also 12.
Compare with A270545, the number of equilateral triangle units forming perimeters of equilateral triangle, which follows the same application.
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LINKS
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FORMULA
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a(0) = 12; thereafter, a(n) = 36*n + 6.
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EXAMPLE
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Illustration of initial terms are found in the three above links.
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MATHEMATICA
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CoefficientList[Series[6 (1 + x) (2 + x)/(1 - x)^2, {x, 0, 40}], x] (* Michael De Vlieger, Mar 23 2016 *)
Join[{12}, 36*Range[50]+6] (* or *) LinearRecurrence[{2, -1}, {12, 42, 78}, 50] (* Harvey P. Dale, Nov 03 2016 *)
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PROG
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(PARI) a(n) = if (!n, 12, 36*n + 6); \\ Michel Marcus, Mar 22 2016
(PARI) Vec(6*(1+x)*(2+x)/(1-x)^2 + O(x^50)) \\ Colin Barker, Mar 22 2016
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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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EXTENSIONS
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STATUS
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approved
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