A014695 - OEIS

%I #46 Apr 17 2023 10:33:59

%S 1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,

%T 2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,

%U 1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1

%N Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of Q_8.

%C From _Klaus Brockhaus_, May 14 2010: (Start)

%C Periodic sequence: Repeat 1, 2, 2, 1.

%C a(n) = A130658(n+1).

%C Continued fraction expansion of (5+sqrt(221))/14.

%C Decimal expansion of 37/303. (End)

%H A. Adem, <a href="http://www.ams.org/notices/199707/adem.pdf">Recent developments in the cohomology of finite groups</a>, Notices Amer. Math. Soc., 44 (1997), 806-812.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

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

%F G.f.: (1+x+x^2)/((1-x)*(1+x^2)) =  (1+2*x+2*x^2+x^3)/(1-x^4).

%F a(n) = (3-sqrt(2)*cos((2*n+1)*Pi/4))/2. - _Jaume Oliver Lafont_, Nov 28 2009

%F a(n) = (6-(1+i)*i^n-(1-i)*(-i)^n)/4 where i = sqrt(-1). - _Klaus Brockhaus_, May 14 2010

%F a(n) = denominator of Sum_{k=0..n} k/2. - _Arkadiusz Wesolowski_, Aug 09 2012

%t Table[Denominator[n*(n + 1)/4], {n, 0, 104}] (* _Arkadiusz Wesolowski_, Aug 09 2012 *)

%t LinearRecurrence[{1,-1,1},{1,2,2},120] (* _Harvey P. Dale_, Jan 19 2020 *)

%o (PARI) x='x+O('x^100); Vec((1+2*x+2*x^2+x^3)/(1-x^4)) \\ _Altug Alkan_, Dec 24 2015

%o (Python)

%o def A014695(n): return (1,2,2,1)[n&3] # _Chai Wah Wu_, Apr 17 2023

%Y Denominators for the sequence whose numerators are A064038.

%Y Cf. A130658, A177841. - _Klaus Brockhaus_, May 14 2010

%K easy,nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Klaus Brockhaus_, May 14 2010