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a(n) = 5*a(n-2) + 2*a(n-3).
4

%I #21 Jan 02 2024 08:57:01

%S 0,0,1,0,5,2,25,20,129,150,685,1008,3725,6410,20641,39500,116025,

%T 238782,659125,1425960,3773189,8448050,21717865,49786628,125485425,

%U 292368870,727000381,1712815200,4219739645,10018076762,24524328625,58529863100

%N a(n) = 5*a(n-2) + 2*a(n-3).

%C a(n+2), n>=0, is the (5,2)-Padovan sequence p(5,2;n)with o.g.f. 1/(1-5*x^2-2*x^3). See A000931(n+3) ((1,1)-Padovan), and the W. Lang link given there, also for a combinatorial interpretation. - _Wolfdieter Lang_, Jun 28 2010

%H G. C. Greubel, <a href="/A135138/b135138.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,2).

%F From _R. J. Mathar_, Feb 15 2008: (Start)

%F O.g.f.: -x^2 / ( (2*x+1)*(x^2+2*x-1) ).

%F a(n) = [(-2)^n + A078343(n)]/7. (End)

%t a = {0, 0, 1}; Do[AppendTo[a, 5*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* _Stefan Steinerberger_, Feb 15 2008 *)

%t LinearRecurrence[{0, 5, 2}, {0, 0, 1}, 100] (* _G. C. Greubel_, Sep 28 2016 *)

%Y Cf. A135139.

%K nonn,easy

%O 0,5

%A _Paul Curtz_, Feb 13 2008

%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Feb 15 2008