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A289999
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Sierpinski cuboctahedral numbers: a(n) = 16*4^n - 12*2^n + 9.
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1
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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
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OFFSET
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0,1
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COMMENTS
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Sierpinski cuboctahedron constructed by joining eight Sierpinski tetrahedra of sequence 4, 10, 34, 130, 514, 2050, 8194... (4^n*2)+2 (the double of A052539). This sequence is also Sierpinski recursion for the octahemioctahedron A274974.
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LINKS
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FORMULA
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a(n) = -3*2^(n + 2) + 2^(2n + 4) + 9.
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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MATHEMATICA
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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 *)
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PROG
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(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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CROSSREFS
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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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