A134771 A134770 interleaved with threes.

1, 3, 5, 3, 21, 3, 77, 3, 277, 3, 1005, 3, 3693, 3, 13725, 3, 51477, 3, 194477, 3, 739021, 3, 2821725, 3, 10816621, 3, 41602397, 3, 160466397, 3, 620470077, 3, 2404321557, 3, 9334424877, 3, 36300541197, 3, 141381055197, 3, 551386115277, 3, 2153031497757, 3

Offset: 0

Author

Gary W. Adamson, Nov 10 2007

Keywords

• nonn
• easy
• less

Comments

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

Second inverse binomial transform of A134770.

A134770 interleaved with threes.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000984, A010701, A134770.

Programs

Magma

A134771:= func< n | (n mod 2) eq 1 select 3 else 2*(n+2)*Catalan(Floor(n/2))-3 >;
[A134771(n): n in [0..50]]; // G. C. Greubel, Oct 13 2023

Mathematica

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

SageMath

def A134771(n): return 4*((n+1)%2)*binomial(n, n//2) - 3*(-1)^n
[A134771(n) for n in range(41)] # G. C. Greubel, Oct 13 2023

Formula

From G. C. Greubel, Oct 13 2023: (Start)

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

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

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

Extensions

Name changed by G. C. Greubel, Oct 13 2023