A139797 - OEIS

%I #6 Mar 08 2021 16:40:22

%S 0,0,0,0,1,1,3,4,10,18,39,75,153,302,608,1212,2429,4853,9711,19416,

%T 38838,77670,155347,310687,621381,1242754,2485516,4971024,9942057,

%U 19884105,39768219,79536428,159072866,318145722,636291455,1272582899,2545165809,5090331606,10180663224,20361326436,40722652885,81445305757

%N Inverse binomial transform of [0, A133474].

%H G. C. Greubel, <a href="/A139797/b139797.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x^4/((1+x)^2 * (1-2*x) * (1-x+x^2)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

%F a(n) = ( (3*n-4)*(-1)^n +2^n +3*ChebyshevU(n, 1/2) -6*ChebyshevU(n-1, 1/2) )/27. - _G. C. Greubel_, Mar 08 2021

%t Table[((3*n-4)*(-1)^n +2^n +3*ChebyshevU[n, 1/2] -6*ChebyshevU[n-1, 1/2])/27, {n, 0, 60}] (* _G. C. Greubel_, Mar 08 2021 *)

%o (Sage) [( (3*n-4)*(-1)^n +2^n +3*chebyshev_U(n, 1/2) -6*chebyshev_U(n-1, 1/2) )/27 for n in (0..60)] # _G. C. Greubel_, Mar 08 2021

%o (Magma)

%o f:= func< n | Evaluate(ChebyshevU(n+1), 1/2) >;

%o [n eq 0 select 0 else ((3*n-4)*(-1)^n +2^n +3*f(n) -6*f(n-1))/27: n in [0..60]]; // _G. C. Greubel_, Mar 08 2021

%Y Cf. A010892.

%K nonn

%O 0,7

%A _Paul Curtz_, May 22 2008

%E Edited by _R. J. Mathar_, Sep 08 2009

%E Terms a(29) onward added by _G. C. Greubel_, Mar 08 2021