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%I #29 Mar 15 2024 02:19:53
%S 8,3,16,5,24,7,32,9,40,11,48,13,56,15,64,17,72,19,80,21,88,23,96,25,
%T 104,27,112,29,120,31,128,33,136,35,144,37,152,39,160,41,168,43,176,
%U 45,184,47,192,49,200,51,208,53,216,55,224,57,232,59,240,61,248,63,256,65,264
%N Multiples of 8 interleaved with the sequence of odd numbers >= 3.
%C For n >= 2, these are the numerators of 1/n^2 - 1/(n+1)^2: A061037(4), A061039(5), A061041(6), A061043(7), A061045(8), A061047(9), A061049(10), etc.
%H Vincenzo Librandi, <a href="/A144433/b144433.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F a(2*n+1) = A008590(n+1), a(2*n) = A005408(n).
%F a(2*n+1) + a(2*n+2) = A017281(n+1).
%F From _R. J. Mathar_, Apr 01 2009: (Start)
%F a(n) = 2*a(n-2) - a(n-4).
%F G.f.: x*(8+3*x-x^3)/((1-x)^2*(1+x)^2). (End)
%F a(n) = (n + 1) * 4^(n mod 2). - _Wesley Ivan Hurt_, Nov 27 2013
%p A144433:=n->(n+1)*4^(n mod 2); seq(A144433(n), n=1..100); # _Wesley Ivan Hurt_, Nov 27 2013
%t Table[(n + 1)* 4^Mod[n, 2], {n, 100}] (* _Wesley Ivan Hurt_, Nov 27 2013 *)
%o (Magma) [5+3/2*(-1)^(n-1)*(n-1)+3*(-1)^(n-1)+5/2*(n-1): n in [1..70]]; // _Vincenzo Librandi_, Jul 30 2011
%o (PARI) x='x+O('x^50); Vec( x*(8+3*x-x^3)/((1-x)^2*(1+x)^2)) \\ _G. C. Greubel_, Sep 19 2018
%Y Cf. A120070.
%K nonn,easy
%O 1,1
%A _Paul Curtz_, Oct 04 2008
%E Edited by _R. J. Mathar_, Apr 01 2009
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