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A061038 Denominator of 1/4 - 1/n^2. 31
1, 36, 16, 100, 9, 196, 64, 324, 25, 484, 144, 676, 49, 900, 256, 1156, 81, 1444, 400, 1764, 121, 2116, 576, 2500, 169, 2916, 784, 3364, 225, 3844, 1024, 4356, 289, 4900, 1296, 5476, 361, 6084, 1600, 6724, 441, 7396, 1936, 8100, 529, 8836 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Harry J. Smith, Table of n, a(n) for n=2..1000

Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

a(4n+2) = (2n+1)^2, a(2n+3) = (4n+6)^2, a(4n+4) = (4n+4)^2. - Ralf Stephan, Jun 10 2005

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12). - Paul Curtz , Feb 25 2011.

From Bruno Berselli, Mar 21 2011:  (Start)

G.f.: x^2*(1+36*x+16*x^2+100*x^3+6*x^4+88*x^5+16*x^6+24*x^7+x^8+4*x^9+4*x^11)/(1-x^4)^3.

a(n) = ( (1/8)*n*(16-(1+(-1)^n)*(5-i^n)) )^2 with i=sqrt(-1).

a(n) = a(n-4)*(n/(n-4))^2 for n>5. (End)

a(n) = 4*n^2 / gcd(4*n^2, (n^2-4)). - Colin Barker, Jan 13 2014

MATHEMATICA

Table[Denominator[1/4 - 1/n^2], {n, 2, 60}] (* Stefan Steinerberger, Apr 08 2006 *)

PROG

(PARI) { for (n=2, 1000, write("b061038.txt", n, " ", denominator(1/4 - 1/n^2)) ) } \\ Harry J. Smith, Jul 17 2009

(MAGMA) [ Denominator(1/4-1/n^2): n in [2..50] ]; // Vincenzo Librandi, Feb 10 2011

(Haskell)

import Data.Ratio ((%), denominator)

a061038 n = denominator (1%4 - 1%n^2)  -- Reinhard Zumkeller, Jan 22 2012

CROSSREFS

See A061037 for comments, references, links.

Cf. A145979. - Bruno Berselli, Mar 21 2011

Sequence in context: A066583 A073405 A056770 * A058231 A008894 A033973

Adjacent sequences:  A061035 A061036 A061037 * A061039 A061040 A061041

KEYWORD

nonn,frac,nice,easy

AUTHOR

N. J. A. Sloane, May 26 2001

EXTENSIONS

More terms from Stefan Steinerberger, Apr 08 2006

STATUS

approved

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Last modified December 21 12:21 EST 2014. Contains 252320 sequences.