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%I #21 Sep 08 2022 08:45:50
%S 0,2,1,6,7,20,33,74,139,288,565,1142,2271,4556,9097,18210,36403,72824,
%T 145629,291278,582535,1165092,2330161,4660346,9320667,18641360,
%U 37282693,74565414,149130799,298261628,596523225,1193046482,2386092931,4772185896
%N a(n) = (5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9.
%H Vincenzo Librandi, <a href="/A172285/b172285.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 (0,3,2).
%F a(n) = 3*a(n-2) + 2*a(n-3), n>2.
%F a(n+1) = 2*a(n) + (-1)^n * (2+n).
%F a(n) = A053088(n-1) + A001045(n), n>0.
%F a(n) = A000079(n) - A053088(n).
%F a(2n) = A141291(n). a(2n+1) = 2*A164044(n).
%F G.f.: x*(2+x)/( (1-2*x)*(1+x)^2 ).
%p A172295 := proc(n) (5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9 ; end proc: seq(A172295(n), n=0..100) ; # _R. J. Mathar_, Feb 02 2010
%t Table[(5*2^n - 5*(-1)^n - 3*n*(-1)^n)/9, {n, 0, 40}] (* _Wesley Ivan Hurt_, Aug 27 2015 *)
%o (Magma) [(5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9: n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2011
%o (PARI) first(m)=vector(m,i,i--;(5*2^i -5*(-1)^i - 3*i*(-1)^i ) / 9) \\ _Anders Hellström_, Aug 27 2015
%Y Cf. A000079, A001045, A053088, A141291, A164044.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Jan 30 2010
%E Definition replaced by explicit formula; g.f. added - _R. J. Mathar_, Feb 02 2010
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