OFFSET
1,2
COMMENTS
a(n) is not divisible by (A114112(n+1)).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(1)=1. a(2n) = n*(2n+1). a(2n+1) = 2n^2 +3n +2.
From R. J. Mathar, Nov 04 2008: (Start)
G.f.: x(1+x+x^2-2x^3+x^4)/((1+x)(1-x)^3).
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>5. (End)
This is (essentially) 1 + A084265, - N. J. A. Sloane, Mar 12 2018
MATHEMATICA
Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {3, 7, 10, 16}, 52]] (* Jean-François Alcover, Sep 22 2017 *)
CoefficientList[Series[(1 + x + x^2 -2 x^3 + x^4)/((1 + x) (1 - x)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Mar 13 2018 *)
PROG
(Magma) I:=[1, 3, 7, 10, 16]; [n le 5 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..60]]; // Vincenzo Librandi, Mar 13 2018
(Python)
def A114113(n): return 1 if n == 1 else (m:=n//2)*(n+1) + (n+1-m)*(n-2*m) # Chai Wah Wu, May 24 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Nov 13 2005
EXTENSIONS
More terms from R. J. Mathar, Aug 31 2007
STATUS
approved