OFFSET
0,2
COMMENTS
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.
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
FORMULA
a(n) = numerator( 1/4 - 1/(5*n-2)^2 ).
From R. J. Mathar, Feb 10 2011: (Start)
a(n) = +3*a(n-4) -3*a(n-8) +a(n-12).
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)
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
MATHEMATICA
f[n_] := n/GCD[n, 4]; Table[ f[n] f[n + 4], {n, -4, 200, 5}] (* Robert G. Wilson v, Feb 03 2011 *)
PROG
(Magma) [ Numerator(1/4-1/(5*n-2)^2): n in [0..40] ]; // Bruno Berselli, Feb 10 2011
(PARI) vector(50, n, n--; numerator( 1/4 - 1/(5*n-2)^2 )) \\ G. C. Greubel, Sep 19 2018
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Paul Curtz, Dec 01 2010
STATUS
approved