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%I #31 Dec 08 2017 18:29:58
%S 14,50,218,938,3914,16010,64778,260618,1045514,4188170,16764938,
%T 67084298,268386314,1073643530,4294770698,17179475978,68718690314,
%U 274876334090,1099508482058,4398040219658,17592173461514,70368719011850,281474926379018,1125899806179338,4503599426043914,18014398106828810
%N Sierpinski stellated octahedron numbers: a(n) = 2*(-3*2^(n+1) + 2^(2n+3) + 5).
%C Stella octangula with Sierpinski recursion.
%H Colin Barker, <a href="/A281699/b281699.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>, see section on higher dimensional analogs.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = 8*(2^(2*n+1)+2) - 6*(2^(n+1)+1).
%F From _Colin Barker_, Jan 28 2017: (Start)
%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2.
%F G.f.: 2*(7 - 24*x + 32*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
%F (End)
%t Table[8 (2^(2 n + 1) + 2) - 6 (2^(n + 1) + 1), {n, 0, 25}] (* or *)
%t LinearRecurrence[{7, -14, 8}, {14, 50, 218}, 26] (* or *)
%t CoefficientList[Series[2 (7 - 24 x + 32 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* _Michael De Vlieger_, Jan 28 2017 *)
%o (PARI) Vec(2*(7 - 24*x + 32*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Jan 28 2017
%o (PARI) a(n) = 16*4^n - 12*2^n + 10 \\ _Charles R Greathouse IV_, Jan 29 2017
%Y Cf. A007588, A027693, A052539, A052548, A067771, A178789, A233774, A279511.
%K nonn,easy
%O 0,1
%A _Steven Beard_, Jan 27 2017