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%I #26 Sep 08 2022 08:46:20
%S 1,6,42,306,2250,16578,122202,900882,6641514,48963042,360969210,
%T 2661166386,19618866954,144635805954,1066295850138,7861032979794,
%U 57953746616490,427251323790882,3149816954720058,23221336706989938,171194226906268746,1262092001672539458
%N a(n) = A299914(2n+1).
%C a(n) is the number of holes shaped like six-pointed stars, in descending size, found in the cross-section, in the shape of a regular hexagon, of a Menger Sponge. - _Albert Säfström_, Jul 25 2018
%D Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
%H Vincenzo Librandi, <a href="/A299916/b299916.txt">Table of n, a(n) for n = 0..200</a>
%H Albert Säfström, <a href="/A299916/a299916.png">Illustration of regular hexagonal cross-section of Menger Sponge, with supporting triangular shape</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-12)
%F G.f.: -(3*x-1)/(12*x^2-9*x+1). - _Alois P. Heinz_, Mar 10 2018
%F From _Colin Barker_, Mar 12 2018: (Start)
%F a(n) = 2^(-1-n)*((9-sqrt(33))^n*(-3+sqrt(33)) + (3+sqrt(33))*(9+sqrt(33))^n) / sqrt(33).
%F a(n) = 9*a(n-1) - 12*a(n-2) for n>1.
%F (End)
%p a:= n-> (<<0|1>, <-12|9>>^n. <<1, 6>>)[1, 1]:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Mar 10 2018
%t CoefficientList[Series[-(3 x - 1)/(12 x^2 - 9 x + 1), {x, 0, 20}], x] (* _Michael De Vlieger_, Mar 10 2018 *)
%t LinearRecurrence[{9, -12}, {1, 6}, 30] (* _Vincenzo Librandi_, Mar 11 2018 *)
%o (Magma) I:=[1,6]; [n le 2 select I[n] else 9*Self(n-1)-12*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Mar 11 2018
%o (PARI) Vec((1 - 3*x) / (1 - 9*x + 12*x^2) + O(x^30)) \\ _Colin Barker_, Mar 12 2018
%Y Cf. A299914.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 10 2018
%E More terms from _Altug Alkan_, Mar 10 2018
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