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%I #20 Dec 31 2018 14:09:08
%S 13,49,217,937,3913,16009,64777,260617,1045513,4188169,16764937,
%T 67084297,268386313,1073643529,4294770697,17179475977,68718690313,
%U 274876334089,1099508482057,4398040219657,17592173461513,70368719011849,281474926379017,1125899806179337,4503599426043913,18014398106828809
%N Sierpinski cuboctahedral numbers: a(n) = 16*4^n - 12*2^n + 9.
%C 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.
%H Colin Barker, <a href="/A289999/b289999.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_triangle#Analogues_in_higher_dimensions">Sierpinski tetrahedron</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = -3*2^(n + 2) + 2^(2n + 4) + 9.
%F From _Colin Barker_, Sep 03 2017: (Start)
%F G.f.: (13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2.
%F (End)
%t 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 *)
%t 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 *)
%o (PARI) Vec((13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Sep 03 2017
%o (PARI) a(n) = 16*4^n - 12*2^n + 9 \\ _Charles R Greathouse IV_, Nov 03 2017
%Y Cf. A005902, A290396, A274974, A281699, A067771, A279511.
%K nonn,easy
%O 0,1
%A _Steven Beard_, Sep 03 2017
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