The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A060762

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A060762

Number of conjugacy classes (the same as the number of irreducible representations) in the dihedral group with 2n elements.
(history; published version)

#22 by Charles R Greathouse IV at Thu Sep 08 08:45:03 EDT 2022

PROG

(MAGMAMagma) [ IsOdd(n) select (n+3)/2 else n/2+3 : n in [1..10] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

Discussion

Thu Sep 08

08:45

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

#21 by Ray Chandler at Fri Jul 31 11:35:39 EDT 2015

STATUS

editing

approved

#20 by Ray Chandler at Fri Jul 31 11:35:36 EDT 2015

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).

STATUS

approved

editing

#19 by Jon E. Schoenfield at Sun Mar 15 14:32:35 EDT 2015

STATUS

editing

approved

#18 by Jon E. Schoenfield at Sun Mar 15 14:32:34 EDT 2015

FORMULA

a(1)=2,a(2)=4. For odd n:a(n)=(a(n-1)+a(n-2))/2; for even n: a(n)=(a(n-1)+a(n-2)+3)/2. [From _Vincenzo Librandi. _, Dec 20 2010]

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {2, 4, 3}, 74] (* Robert G. Wilson v, Apr 19, 2012 *)

PROG

(MAGMA) [ IsOdd(n) select (n+3)/2 else n/2+3 : n in [1..10] ]; - from // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

(PARI) { for (n=1, 1000, if (n%2, a=(n + 3)/2, a=(n + 6)/2); write("b060762.txt", n, " ", a); ) } [From _\\ _Harry J. Smith_, Jul 11 2009]

STATUS

approved

editing

#17 by N. J. A. Sloane at Thu Oct 31 12:17:18 EDT 2013

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {2, 4, 3}, 74] (* _Robert G. Wilson v, _, Apr 19, 2012 *)

Discussion

Thu Oct 31

12:17

OEIS Server: https://oeis.org/edit/global/2036

#16 by T. D. Noe at Thu Apr 19 17:33:04 EDT 2012

STATUS

editing

approved

#15 by Robert G. Wilson v at Thu Apr 19 16:30:22 EDT 2012

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {2, 4, 3}, 74] (* Robert G. Wilson v, Apr 19, 2012 *)

STATUS

proposed

editing

#14 by Colin Barker at Thu Apr 19 14:07:01 EDT 2012

STATUS

editing

proposed

#13 by Colin Barker at Thu Apr 19 14:06:53 EDT 2012

FORMULA

a(n)=a(n-1)+a(n-2)-a(n-3). G.f.: x*(2+2*x-3*x^2)/((1-x)^2*(1+x)). [Colin Barker, Apr 19 2012]

MATHEMATICA

a[1] = 2; a[2] = 4; a[n_] := a[n] = (a[n - 1] + a[n - 2] + If[ OddQ@ n, 0, 3])/2; Array[a, 74]

KEYWORD

nonn,easy

STATUS

approved

editing