A026395 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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]

LINKS

Table of n, a(n) for n=0..29.

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

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

Cf. A000010, A026386.

Sequence in context: A151523 A317708 A265264 * A247630 A015889 A090246

Adjacent sequences: A026392 A026393 A026394 * A026396 A026397 A026398

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Better name from Ralf Stephan, Jul 17 2013

STATUS

approved