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A061038
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Denominator of 1/4 - 1/n^2.
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25
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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;
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refs;
listen;
history;
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internal format)
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OFFSET
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2,2
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LINKS
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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).
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FORMULA
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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.
Contribution 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)
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MATHEMATICA
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Table[Denominator[1/4 - 1/n^2], {n, 2, 60}] - Stefan Steinerberger, Apr 08 2006
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PROG
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(PARI) { for (n=2, 1000, write("b061038.txt", n, " ", denominator(1/4 - 1/n^2)) ) } [From 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
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CROSSREFS
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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
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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N. J. A. Sloane, May 26 2001
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EXTENSIONS
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More terms from Stefan Steinerberger, Apr 08 2006
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STATUS
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approved
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