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%I #23 Sep 08 2022 08:45:51
%S 0,5,15,165,20,525,195,1085,90,1845,575,2805,210,3965,1155,5325,380,
%T 6885,1935,8645,600,10605,2915,12765,870,15125,4095,17685,1190,20445,
%U 5475,23405,1560,26565,7055,29925,1980,33485,8835,37245,2450
%N Quintisection A061037(5*n-2).
%C All entries are multiples of 5. Like A061037(n+2), the (2k+1)-sections A061037((2*k+1)*n-2) are multiples of 2k+1; see A165248, A165943.
%C The sequence contains 4 interlaced second-order polynomials: a(4n) = 5n*(5n-1), a(4n+1) = 5*(4n+1)*(20n+1), a(4n+2)= 5*(2n+1)*(10n+3), a(4n+3)= 5*(4n+3)*(20n+11). - _R. J. Mathar_, Feb 10 2011
%H Vincenzo Librandi, <a href="/A174850/b174850.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
%F a(n) = numerator( 1/4 - 1/(5*n-2)^2 ).
%F From _R. J. Mathar_, Feb 10 2011: (Start)
%F a(n) = +3*a(n-4) -3*a(n-8) +a(n-12).
%F G.f. ( -5*x*(1+3*x+33*x^2+4*x^3+102*x^4+30*x^5+118*x^6+6*x^7+57*x^8 +7*x^9+9*x^10) )/( (x-1)^3*(1+x)^3*(x^2+1)^3 ). (End)
%F a(n) = 5*n*(5*n-4)*(37-27*(-1)^n-3*(-i)^n-3*i^n)/64, where i=sqrt(-1). - _Bruno Berselli_, Feb 10 2011
%t f[n_] := n/GCD[n, 4]; Table[ f[n] f[n + 4], {n, -4, 200, 5}] (* _Robert G. Wilson v_, Feb 03 2011 *)
%o (Magma) [ Numerator(1/4-1/(5*n-2)^2): n in [0..40] ]; // _Bruno Berselli_, Feb 10 2011
%o (PARI) vector(50, n, n--; numerator( 1/4 - 1/(5*n-2)^2 )) \\ _G. C. Greubel_, Sep 19 2018
%K nonn,easy,frac
%O 0,2
%A _Paul Curtz_, Dec 01 2010
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