A134771 - OEIS

%I #20 Oct 14 2023 06:56:33

%S 1,3,5,3,21,3,77,3,277,3,1005,3,3693,3,13725,3,51477,3,194477,3,

%T 739021,3,2821725,3,10816621,3,41602397,3,160466397,3,620470077,3,

%U 2404321557,3,9334424877,3,36300541197,3,141381055197,3,551386115277,3,2153031497757,3

%N A134770 interleaved with threes.

%C Previous name was: A007318^(-2) * A134770.

%C Second inverse binomial transform of A134770.

%C A134770 interleaved with threes.

%H G. C. Greubel, <a href="/A134771/b134771.txt">Table of n, a(n) for n = 0..1000</a>

%F From _G. C. Greubel_, Oct 13 2023: (Start)

%F a(n) = 2*(1 + (-1)^n)*binomial(n, n/2) - 3*(-1)^n.

%F G.f.: 2/sqrt(1-4*x^2) - 3/(1+x).

%F E.g.f.: 4*BesselI(0, 2*x) - 3*exp(-x). (End)

%e First few terms of the sequence are (1, 3, 5, 3, 21, 3, 77, ...), since A134770 = (1, 3, 5, 21, 77, ...).

%t Table[If[OddQ[n], 3, 4*Binomial[n,n/2] -3], {n,0,50}] (* _G. C. Greubel_, Oct 13 2023 *)

%o (Magma)

%o A134771:= func< n | (n mod 2) eq 1 select 3 else 2*(n+2)*Catalan(Floor(n/2))-3 >;

%o [A134771(n): n in [0..50]]; // _G. C. Greubel_, Oct 13 2023

%o (SageMath)

%o def A134771(n): return 4*((n+1)%2)*binomial(n, n//2) - 3*(-1)^n

%o [A134771(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2023

%Y Cf. A000984, A010701, A134770.

%K nonn,easy,less

%O 0,2

%A _Gary W. Adamson_, Nov 10 2007

%E Name changed by _G. C. Greubel_, Oct 13 2023