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A112033 a(n) = 3 * 2^(floor(n/2) + 1 + (-1)^n).

%I A112033 #41 May 11 2025 01:10:01
%S A112033 12,3,24,6,48,12,96,24,192,48,384,96,768,192,1536,384,3072,768,6144,
%T A112033 1536,12288,3072,24576,6144,49152,12288,98304,24576,196608,49152,
%U A112033 393216,98304,786432,196608,1572864,393216,3145728,786432,6291456,1572864
%N A112033 a(n) = 3 * 2^(floor(n/2) + 1 + (-1)^n).
%D A112033 George Pólya and Gábor Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chapter 4, Sect. 1, Problem 148.
%H A112033 Reinhard Zumkeller, <a href="/A112033/b112033.txt">Table of n, a(n) for n = 0..100</a>
%H A112033 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A112033 a(n) = 1 / abs(A112031(n)/A112032(n) - 2/3). (previous name)
%F A112033 a(n) = 3*2^A084964(n) = 3*A112032(n).
%F A112033 From _Ralf Stephan_, Jul 16 2013: (Start)
%F A112033 Recurrence: a(n) = 2a(n-2), a(0)=12, a(1)=3.
%F A112033 G.f.: (6*x+24)/(1-2*x^2). (End)
%F A112033 From _Amiram Eldar_, May 11 2025: (Start)
%F A112033 Sum_{n>=0} 1/a(n) = 5/6.
%F A112033 Sum_{n>=0} (-1)^n/a(n) = -1/2. (End)
%p A112033 A112033:=n->3*2^(floor(n/2) + 1 + (-1)^n); seq(A112033(k), k=0..50); # _Wesley Ivan Hurt_, Nov 01 2013
%t A112033 Table[3*2^(Floor[n/2] + 1 + (-1)^n), {n,0,50}] (* _Wesley Ivan Hurt_, Nov 01 2013 *)
%o A112033 (PARI) a(n) = 3 * 2^(n\2 + 1 + (-1)^n); \\ _Michel Marcus_, Nov 02 2013
%o A112033 (Python)
%o A112033 def A112033(n): return 3*(1<<(n>>1)+(int(not n&1)<<1)) # _Chai Wah Wu_, Jan 17 2023
%Y A112033 Cf. A084964, A112030, A112031, A112032.
%K A112033 nonn,easy
%O A112033 0,1
%A A112033 _Reinhard Zumkeller_, Aug 27 2005