The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A134763

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A134763

a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).
(history; published version)

#11 by OEIS Server at Tue May 28 18:28:19 EDT 2024

LINKS

G. C. Greubel, <a href="/A134763/b134763_1.txt">Table of n, a(n) for n = 0..1000</a>

#10 by Michael De Vlieger at Tue May 28 18:28:19 EDT 2024

STATUS

reviewed

approved

Discussion

Tue May 28

18:28

OEIS Server: Installed first b-file as b134763.txt.

#9 by Michel Marcus at Tue May 28 09:44:28 EDT 2024

STATUS

proposed

reviewed

#8 by G. C. Greubel at Tue May 28 04:19:18 EDT 2024

STATUS

editing

proposed

#7 by G. C. Greubel at Tue May 28 04:19:11 EDT 2024

CROSSREFS

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

STATUS

proposed

editing

#6 by G. C. Greubel at Tue May 28 04:12:38 EDT 2024

STATUS

editing

proposed

Discussion

Tue May 28

04:16

G. C. Greubel: Similar to A134761: With the original name I struggled to make it work as suggested. Changed the name to one that makes more sense with the comments and data. Additional components added to make the sequence into something usable.

#5 by G. C. Greubel at Tue May 28 04:12:32 EDT 2024

NAME

A000718^(-2) * A134762.

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

DATA

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

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, <a href="/A134763/b134763_1.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

Second inverse binomial transform of A134762. A134762 interpolated with two's.

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)

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. A134762, A000718, A000984, A001405, A134758, A134759, A134760, A134761, A134762.

EXTENSIONS

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

STATUS

approved

editing

#4 by Jon E. Schoenfield at Sat Mar 26 03:49:52 EDT 2022

STATUS

editing

approved

#3 by Jon E. Schoenfield at Sat Mar 26 03:49:50 EDT 2022

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, ...).

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:25:26 EDT 2012

AUTHOR

_Gary W. Adamson (qntmpkt(AT)yahoo.com), _, Nov 09 2007

Discussion

Fri Mar 30

17:25

OEIS Server: https://oeis.org/edit/global/135