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A026395
a(n) = 5*a(n-2), starting 1,2,4.
1
1, 2, 4, 10, 20, 50, 100, 250, 500, 1250, 2500, 6250, 12500, 31250, 62500, 156250, 312500, 781250, 1562500, 3906250, 7812500, 19531250, 39062500, 97656250, 195312500, 488281250, 976562500, 2441406250, 4882812500, 12207031250
OFFSET
0,2
COMMENTS
T(n,0) + T(n,1) + ... + T(n,n), where T is array in A026386.
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]
FORMULA
G.f.: (1+2*x-x^2)/(1-5*x^2). - Ralf Stephan, Apr 30 2004
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
For n > 3: a(n) = a(n-2)*a(n-1)/a(n). - Reinhard Zumkeller, Mar 06 2011
MATHEMATICA
LinearRecurrence[{0, 5}, {1, 2, 4}, 50] (* Paolo Xausa, Feb 02 2024 *)
CROSSREFS
Sequence in context: A151523 A317708 A265264 * A247630 A015889 A090246
KEYWORD
nonn,easy
EXTENSIONS
Better name from Ralf Stephan, Jul 17 2013
STATUS
approved