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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 (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]

CROSSREFS

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

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)