|
%I #30 Feb 02 2024 09:01:01
%S 1,2,4,10,20,50,100,250,500,1250,2500,6250,12500,31250,62500,156250,
%T 312500,781250,1562500,3906250,7812500,19531250,39062500,97656250,
%U 195312500,488281250,976562500,2441406250,4882812500,12207031250
%N a(n) = 5*a(n-2), starting 1,2,4.
%C T(n,0) + T(n,1) + ... + T(n,n), where T is array in A026386.
%C a(n) is the number of irreducible representations of the Heisenberg group over the Gaussian integers into complex matrices of size 5^n x 5^n. [From Shannon Ezzat (sez10(AT)math.canterbury.ac.nz), Jan 20 2009]
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,5).
%F G.f.: (1+2*x-x^2)/(1-5*x^2). - _Ralf Stephan_, Apr 30 2004
%F a(n) = a(n-1) + 2*5^(n/2 -1) if n is even, a(n) = a(n-2) + 2*phi(5^[(n-1)/2]) if n is odd, where phi is the Euler phi function. - Shannon Ezzat (sez10(AT)math.canterbury.ac.nz), Jan 20 2009
%F For n > 3: a(n) = a(n-2)*a(n-1)/a(n). - _Reinhard Zumkeller_, Mar 06 2011
%t LinearRecurrence[{0, 5}, {1, 2, 4}, 50] (* _Paolo Xausa_, Feb 02 2024 *)
%Y Cf. A000010, A026386.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
%E Better name from _Ralf Stephan_, Jul 17 2013
|
