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 A270700 Triangular Star of David numbers (the figurate number of triangles framing a hexagram: a(0) = 12; thereafter a(n) = 36*n+6). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Peter M. Chema, Illustration of a(2)=78 Peter M. Chema, Illustration of initial terms [0 through 5] Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(0) = 12; thereafter, a(n) = 36*n + 6. a(n) = 2*a(n-1)-a(n-2) for n>2. - Colin Barker, Mar 22 2016 G.f.: 6*(1+x)*(2+x) / (1-x)^2. - Colin Barker, Mar 22 2016 EXAMPLE Illustration of initial terms are found in the three above links. MATHEMATICA 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 *) PROG (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 (MAGMA) [12] cat [36*n + 6: n in [1..50]]; // Vincenzo Librandi, Mar 28 2016 CROSSREFS Cf. A270545, A045945, A045943 and A045946. Sequence in context: A109275 A241854 A085798 * A282693 A045945 A210206 Adjacent sequences:  A270697 A270698 A270699 * A270701 A270702 A270703 KEYWORD nonn,easy AUTHOR Peter M. Chema, Mar 21 2016 EXTENSIONS More terms from Vincenzo Librandi, Mar 28 2016 STATUS approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)