The On-Line Encyclopedia of Integer Sequences (OEIS)

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A154383

Powers of 4 at even indices, two times powers of 4 at odd indices.
(history; published version)

#14 by Charles R Greathouse IV at Thu Sep 08 08:45:40 EDT 2022

PROG

(MAGMAMagma) [1, 0] cat [(5+3*(-1)^n)*2^(n-3): n in [2..40]]; // Vincenzo Librandi, Sep 16 2016

Discussion

Thu Sep 08

08:45

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

#13 by R. J. Mathar at Sun Mar 04 08:14:44 EST 2018

STATUS

editing

approved

#12 by R. J. Mathar at Sun Mar 04 08:14:40 EST 2018

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).

STATUS

approved

editing

#11 by Bruno Berselli at Fri Sep 16 02:42:52 EDT 2016

STATUS

proposed

approved

#10 by Vincenzo Librandi at Fri Sep 16 00:35:30 EDT 2016

STATUS

editing

proposed

#9 by Vincenzo Librandi at Fri Sep 16 00:35:20 EDT 2016

PROG

(MAGMA) [1, 0] cat [(5+3*(-1)^n)*2^(n-3): n in [2..40]]; // Vincenzo Librandi, Sep 16 2016

STATUS

reviewed

editing

#8 by Michel Marcus at Fri Sep 16 00:26:52 EDT 2016

STATUS

proposed

reviewed

#7 by G. C. Greubel at Thu Sep 15 23:30:18 EDT 2016

STATUS

editing

proposed

#6 by G. C. Greubel at Thu Sep 15 23:30:11 EDT 2016

DATA

1, 0, 4, 2, 16, 8, 64, 32, 256, 128, 1024, 512, 4096, 2048, 16384, 8192, 65536, 32768, 262144, 131072, 1048576, 524288, 4194304, 2097152, 16777216, 8388608, 67108864, 33554432, 268435456, 134217728, 1073741824, 536870912, 4294967296, 2147483648, 17179869184, 8589934592, 68719476736, 34359738368, 274877906944, 137438953472

#5 by G. C. Greubel at Thu Sep 15 23:29:33 EDT 2016

DATA

LINKS

G. C. Greubel, <a href="/A154383/b154383.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(2n) = A131577(2n+1); a(2n+1) = A131577(2n) (Consecutive terms of A131577 swapped).

a(2n) = A000302(n); a(2n+1) = A000302(n)/2, n>0.

a(n) =4a 4*a(n-2), n>3.

a(2n+1) = a(2n)/2, n>0.

G.f.: (1 + 2*x^3)/((1-2*x)*(2*x+1)). a(n)=(5+3*(-1)^n)*2^(n-3), n>1. [ _R. J. Mathar, _, May 21 2009]

a(n) = (5 + 3*(-1)^n)*2^(n-3), n>1. - R. J. Mathar, May 21 2009

E.g.f.: (1/4)*(-2*x + sinh(2*x) + 4*cosh(2*x)). - G. C. Greubel, Sep 15 2016

MATHEMATICA

Join[{1, 0}, Table[(5 + 3*(-1)^n)*2^(n - 3), {n, 2, 20}]] (* G. C. Greubel, Sep 15 2016 *)

STATUS

approved

editing