A270700 Triangular Star of David numbers (the figurate number of triangles framing a hexagram: a(0) = 12; thereafter a(n) = 36*n + 6).
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
Offset: 0
Examples
Illustration of initial terms are found in the three above links.
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).
![Illustration of initial terms [0 through 5]](/A270700/a270700_2.png){kind=link}
Programs
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Magma
[12] cat [36*n + 6: n in [1..50]]; // Vincenzo Librandi, Mar 28 2016
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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 *) -
PARI
a(n) = if (!n, 12, 36*n + 6); \\ Michel Marcus, Mar 22 2016
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PARI
Vec(6*(1+x)*(2+x)/(1-x)^2 + O(x^50)) \\ Colin Barker, Mar 22 2016
Formula
a(0) = 12; thereafter, a(n) = 36*n + 6.
From Colin Barker, Mar 22 2016: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 2.
G.f.: 6*(1+x)*(2+x)/(1-x)^2. (End)
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: 6*(exp(x)*(6*x + 1) + 1).
a(n) = 6*A271114(n). (End)
Extensions
More terms from Vincenzo Librandi, Mar 28 2016
Comments