A134389 - OEIS

%I #13 Apr 11 2021 04:16:34

%S 1,2,5,11,24,51,108,226,472,979,2028,4182,8616,17694,36312,74340,

%T 152112,310659,634188,1292686,2633992,5360362,10905480,22163676,

%U 45032784,91417646,185539448,376279196

%N A transform of floor((n+2)/2) with Hankel transform floor((n+2)/2)*(cos(Pi*n/2) + sin(Pi*n/2)).

%C Transform of floor((n+2)/2) = 1,1,2,2,3,3,4,4,... (A008619) under the array A134388. Hankel transform is the signed version of A008619 given by 1,1,-2,-2,3,3,-4,4,....

%F G.f.: ((2-x)/(1-2*x) + x*sqrt(1-4*x^2)/(1-2*x)^2)/2.

%F Conjecture: (n-1)*a(n) - 2*n*a(n-1) + 4*(4-n)*a(n-2) + 8*(n-3)*a(n-3) = 0. - _R. J. Mathar_, Oct 25 2012

%F a(n) ~ 2^(n - 1/2) * sqrt(n/Pi) * (1 + 3*sqrt(2*Pi/n)/4). - _Vaclav Kotesovec_, Apr 11 2021

%Y Cf. A008619, A134388.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 23 2007