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A172160 a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0. 2

%I #19 Apr 22 2022 17:55:20

%S 1,2,3,4,4,0,-16,-64,-192,-512,-1280,-3072,-7168,-16384,-36864,-81920,

%T -180224,-393216,-851968,-1835008,-3932160,-8388608,-17825792,

%U -37748736,-79691776,-167772160,-352321536,-738197504,-1543503872,-3221225472,-6710886400

%N a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0.

%C The inverse binomial transform is 1,1,0,0,-1,-1,-2,-2,-3,-3 = essentially A168050 or the negative of A004526.

%H Vincenzo Librandi, <a href="/A172160/b172160.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).

%F a(n+1) - 2*a(n) = -A131577(n).

%F a(n) + A001787(n-1) = A000079(n+1).

%F a(n+5) = -A059165(n) = 4*A159964(n+1).

%F G.f.: (1 - 2*x - x^2)/(1-2*x)^2. - _R. J. Mathar_, Feb 11 2010

%F a(n) = 4*a(n-1) - 4*a(n-2), n>2.

%F E.g.f.: (1/4)*((5-2*x)*exp(2*x) - 1). - _G. C. Greubel_, Apr 21 2022

%F a(n) = 4^n*A045891(1-n) if n>1. - _Michael Somos_, Apr 22 2022

%e G.f. = 1 + 2*x + 3*x^2 + 4*x^3 + 4*x^4 - 16*x^6 - 64*x^7 + ... - _Michael Somos_, Apr 22 2022

%t Table[2^(n-2)*(5-n) -(1/4)*Boole[n==0], {n,0,40}] (* _G. C. Greubel_, Apr 21 2022 *)

%o (SageMath) [2^(n-2)*(5-n) -(1/4)*bool(n==0) for n in (1..40)] # _G. C. Greubel_, Apr 21 2022

%Y Cf. A004526, A045891, A168050.

%Y Cf. A000079, A001787, A059165, A159964, A131577.

%K sign,easy

%O 0,2

%A _Paul Curtz_, Jan 27 2010

%E Definition replaced with closed form by _R. J. Mathar_, Feb 11 2010

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)