A026395 a(n) = 5*a(n-2), starting 1,2,4.

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

Author

Clark Kimberling

Keywords

• nonn
• easy

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]

Links

• Index entries for linear recurrences with constant coefficients, signature (0,5).

Crossrefs

Cf. A000010, A026386.

Programs

Mathematica

LinearRecurrence[{0, 5}, {1, 2, 4}, 50] (* Paolo Xausa, Feb 02 2024 *)

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

Extensions

Better name from Ralf Stephan, Jul 17 2013