A134763 a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).

1, 2, 4, 2, 16, 2, 58, 2, 208, 2, 754, 2, 2770, 2, 10294, 2, 38608, 2, 145858, 2, 554266, 2, 2116294, 2, 8112466, 2, 31201798, 2, 120349798, 2, 465352558, 2, 1803241168, 2, 7000818658, 2, 27225405898, 2, 106035791398, 2, 413539586458, 2, 1614773623318, 2, 6312296891158, 2

Offset

0,2

Comments

Second inverse binomial transform of A134762.

A134762 interpolated with two's.

Former name: A000718^(-2) * A134762. - G. C. Greubel, May 28 2024

Links

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

Formula

From G. C. Greubel, May 28 2024: (Start)

a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).

a(n) = (3/2)*(1+(-1)^n)*A001405(n) - 2*(-1)^n.

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

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

Example

First few terms of the sequence are: (1, 2, 4, 2, 16, 2, 58, ...), interpolating two's in the sequence A134762: (1, 4, 16, 58, ...).

Mathematica

Table[(3/2)*(1+(-1)^n)*Binomial[n, n/2] -2*(-1)^n, {n, 0, 40}] (* G. C. Greubel, May 28 2024 *)

Prog

(Magma) [3*((n+1) mod 2)*Binomial(n, Floor(n/2)) - 2*(-1)^n : n in [0..40]]; // G. C. Greubel, May 28 2024
(SageMath) [3*((n+1)%2)*binomial(n, n//2) - 2*(-1)^n for n in range(41)] # G. C. Greubel, May 28 2024

Crossrefs

Cf. A000718, A000984, A001405, A134758, A134759, A134760, A134761, A134762, A134770, A134771.

Sequence in context: A215055 A152877 A071353 * A370135 A290645 A152878

Adjacent sequences: A134760 A134761 A134762 * A134764 A134765 A134766

Keyword

nonn

Author

Gary W. Adamson, Nov 09 2007

Extensions

Name change and terms a(14) onward added by G. C. Greubel, May 28 2024

Status

approved