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A061038
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Denominator of 1/4 - 1/n^2.
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32
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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;
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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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Index entries for 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
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) = (1/64)*( n*(16 - (1+(-1)^n)*(5-i^n)) )^2 with i=sqrt(-1).
a(n) = (n/(n-4))^2 * a(n-4) for n>5. (End)
a(n) = 4*n^2 / gcd(4*n^2, (n^2-4)). - Colin Barker, Jan 13 2014
Sum_{n>=2} 1/a(n) = Pi^2/6 - 1/4. - Amiram Eldar, Aug 12 2022
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 36, 16, 100, 9, 196, 64, 324, 25, 484, 144, 676}, 50] (* Harvey P. Dale, Aug 05 2018 *)
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PROG
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(PARI) { for (n=2, 1000, write("b061038.txt", n, " ", denominator(1/4 - 1/n^2)) ) } \\ Harry J. Smith, Jul 17 2009
(Haskell)
import Data.Ratio ((%), denominator)
(SageMath)
def A061038(n): return denominator(1/4 - 1/n^2)
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CROSSREFS
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See A061037 for comments, references, links.
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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