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Revision History for A123169

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A123169

Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1).
(history; published version)

#22 by OEIS Server at Thu Jul 20 11:15:53 EDT 2023

LINKS

G. C. Greubel, <a href="/A123169/b123169_1.txt">Table of n, a(n) for n = 1..1000</a>

#21 by Alois P. Heinz at Thu Jul 20 11:15:53 EDT 2023

STATUS

proposed

approved

Discussion

Thu Jul 20

11:15

OEIS Server: Installed first b-file as b123169.txt.

#20 by G. C. Greubel at Thu Jul 20 03:52:45 EDT 2023

STATUS

editing

proposed

#19 by G. C. Greubel at Thu Jul 20 03:52:42 EDT 2023

PROG

(Magma) [n eq 1 select 1 0 else (3 + (-1)^n)*(2*n-3): n in [1..100]]; // G. C. Greubel, Jul 19 2023

STATUS

proposed

editing

#18 by G. C. Greubel at Wed Jul 19 23:19:43 EDT 2023

STATUS

editing

proposed

Discussion

Thu Jul 20

00:25

Michel Marcus: magma should be n eq 1 select 0 ?

#17 by G. C. Greubel at Wed Jul 19 23:19:39 EDT 2023

LINKS

G. C. Greubel, <a href="/A123169/b123169_1.txt">Table of n, a(n) for n = 1..1000</a>

CROSSREFS

Cf. A123168.

#16 by G. C. Greubel at Wed Jul 19 23:15:38 EDT 2023

FORMULA

a(1) = 0, for n >= 1 , a(2n2*n) =16n 16*n - 12, a(2n2*n+1) =8n 8*n - 2.

a(n) = (3+(-1)^n)*(-3+2*n) for n>1. a(n) = 2*a(n-2)-a(n-4) for n>5. G.f.: 2*x^2*(x^3+6*x^2+3*x+2) / ((x-1)^2*(x+1)^2). - Colin Barker, Jun 28 2013

From Colin Barker, Jun 28 2013: (Start)

a(n) = (3 + (-1)^n)*(-3 + 2*n) for n > 1.

a(n) = 2*a(n-2) - a(n-4) for n > 5.

G.f.: 2*x^2*(2+3*x+6*x^2+x^3)/((1-x)^2*(1+x)^2). (End)

MATHEMATICA

LinearRecurrence[{0, 2, 0, -1}, {0, 4, 6, 20, 14}, 100] (* G. C. Greubel, Jul 19 2023 *)

PROG

(Magma) [n eq 1 select 1 else (3 + (-1)^n)*(2*n-3): n in [1..100]]; // G. C. Greubel, Jul 19 2023

(SageMath) [(3+(-1)^n)*(2*n-3) + 2*int(n==1) for n in range(1, 101)] # G. C. Greubel, Jul 19 2023

STATUS

approved

editing

#15 by N. J. A. Sloane at Thu Apr 27 22:49:50 EDT 2017

STATUS

proposed

approved

#14 by Wesley Ivan Hurt at Thu Apr 27 22:09:00 EDT 2017

STATUS

editing

proposed

#13 by Wesley Ivan Hurt at Thu Apr 27 22:08:50 EDT 2017

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

FORMULA

a(n) = (3+(-1)^n)*(-3+2*n) for n>1. a(n) = 2*a(n-2)-a(n-4) for n>5. G.f.: 2*x^2*(x^3+6*x^2+3*x+2) / ((x-1)^2*(x+1)^2). - Colin Barker, Jun 28 2013

MAPLE

A123169:=n->(3+(-1)^n)*(-3+2*n): 0, seq(A123169(n), n=2..100); # Wesley Ivan Hurt, Apr 27 2017

STATUS

approved

editing