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

0,2

Comments

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

Second inverse binomial transform of A134770.

A134770 interleaved with threes.

Links

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

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)

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000984, A010701, A134770.

Sequence in context: A014782 A348591 A094466 * A080349 A249012 A249908

Adjacent sequences: A134768 A134769 A134770 * A134772 A134773 A134774

Keyword

nonn,easy,less

Author

Gary W. Adamson, Nov 10 2007

Extensions

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

Status

approved