A289999 Sierpinski cuboctahedral numbers: a(n) = 16*4^n - 12*2^n + 9.
13, 49, 217, 937, 3913, 16009, 64777, 260617, 1045513, 4188169, 16764937, 67084297, 268386313, 1073643529, 4294770697, 17179475977, 68718690313, 274876334089, 1099508482057, 4398040219657, 17592173461513, 70368719011849, 281474926379017, 1125899806179337, 4503599426043913, 18014398106828809
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Wikipedia, Sierpinski tetrahedron.
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Programs
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Mathematica
CoefficientList[Series[(13 - 42 x + 56 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* Michael De Vlieger, Sep 03 2017 *) Table[16*4^n-12*2^n+9,{n,0,30}] (* or *) LinearRecurrence[{7,-14,8},{13,49,217},30] (* Harvey P. Dale, Dec 31 2018 *) -
PARI
Vec((13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Sep 03 2017
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PARI
a(n) = 16*4^n - 12*2^n + 9 \\ Charles R Greathouse IV, Nov 03 2017
Formula
a(n) = -3*2^(n + 2) + 2^(2n + 4) + 9.
From Colin Barker, Sep 03 2017: (Start)
G.f.: (13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2.
(End)
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