OFFSET
1,2
COMMENTS
If b(n) is the sequence of integers congruent to {0,3} (mod 5) and c(n) is the sequence of integers congruent to {2,4}(mod 5). Then a(n) = b(n) + c(n). Equivalently a(n) = A047218(n+1) + A047211(n). - Anthony Hernandez, Aug 16 2016
LINKS
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 10*n - a(n-1) - 16 for n>2, with a(1)=0, a(2)=5. - Vincenzo Librandi, Aug 07 2010
From Colin Barker, Sep 26 2012: (Start)
a(n) = ((-1)^n + 10*n - 11)/2 for n>1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.
G.f.: x^2*(5+4*x+x^2)/((1-x)^2*(1+x)). (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(5+2*sqrt(5))*Pi/20 - 3*sqrt(5)*log(phi)/20 - log(5)/8, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023
MATHEMATICA
Rest@ CoefficientList[Series[x^2*(5 + 4 x + x^2)/((1 - x)^2*(1 + x)), {x, 0, 50}], x] (* Michael De Vlieger, Aug 26 2016 *)
LinearRecurrence[{1, 1, -1}, {0, 5, 9, 15}, 50] (* Harvey P. Dale, Apr 09 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 08 2001
STATUS
approved