The On-Line Encyclopedia of Integer Sequences (OEIS)

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A164587

a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.
(history; published version)

#9 by Ray Chandler at Fri Jun 30 01:04:42 EDT 2023

STATUS

editing

approved

#8 by Ray Chandler at Fri Jun 30 01:04:39 EDT 2023

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2).

STATUS

approved

editing

#7 by Charles R Greathouse IV at Thu Sep 08 08:45:47 EDT 2022

PROG

(MAGMAMagma) [ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#6 by Joerg Arndt at Sun Aug 13 02:27:39 EDT 2017

STATUS

reviewed

approved

#5 by Michel Marcus at Sat Aug 12 15:54:15 EDT 2017

STATUS

proposed

reviewed

#4 by G. C. Greubel at Sat Aug 12 15:35:57 EDT 2017

STATUS

editing

proposed

#3 by G. C. Greubel at Sat Aug 12 15:35:38 EDT 2017

LINKS

G. C. Greubel, <a href="/A164587/b164587.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

a(n) = (5 + 3*(-1)^n)*2^(1/4*(2*n -5 +(-1)^n)/4).

E.g.f.: 4*cosh(sqrt(2)*x) + (1/sqrt(2))*sinh(sqrt(2)*x) - 4. - G. C. Greubel, Aug 12 2017

MATHEMATICA

CoefficientList[Series[(1 - x)/(1 - 10*x + 17*x^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(x*(1+8*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 12 2017

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:28:03 EDT 2012

AUTHOR

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Aug 17 2009

Discussion

Fri Mar 30

17:28

OEIS Server: https://oeis.org/edit/global/145

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.

DATA

1, 8, 2, 16, 4, 32, 8, 64, 16, 128, 32, 256, 64, 512, 128, 1024, 256, 2048, 512, 4096, 1024, 8192, 2048, 16384, 4096, 32768, 8192, 65536, 16384, 131072, 32768, 262144, 65536, 524288, 131072, 1048576, 262144, 2097152, 524288, 4194304, 1048576

OFFSET

1,2

COMMENTS

Interleaving of A000079 and A000079 without initial terms 1, 2, 4.

Binomial transform is A048696. Second binomial transform is A164298.

FORMULA

a(n) = (5+3*(-1)^n)*2^(1/4*(2*n-5+(-1)^n)).

G.f.: x*(1+8*x)/(1-2*x^2).

PROG

(MAGMA) [ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];

CROSSREFS

Equals A112032 without initial term 4.

Cf. A000079 (powers of 2), A048696, A164298.

KEYWORD

nonn

AUTHOR

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009

STATUS

approved