OFFSET
1,1
COMMENTS
Conjecture: For no term n>2 in the sequence 36*n^2+72*n+35 is equal to p*(p+2), where p, p+2 are twin primes.
The conjecture is evident, it can be proved as in A169599. [Bruno Berselli, Jan 07 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Jul 11 2012
a(n) = (34*n +5*(-1)^n -21)/4. - Vincenzo Librandi, Jan 06 2013, modified Jul 07 2015
G.f.: x*(2+11*x+4*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015
MATHEMATICA
Select[Range[489], MemberQ[{2, 13}, Mod[#, 17]]&] (* Ray Chandler, Jul 08 2015 *)
LinearRecurrence[{1, 1, -1}, {2, 13, 19}, 58] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(2+11*x+4*x^2)/((1+x)*(x-1)^2), {x, 0, 58}], x]] (* Ray Chandler, Jul 08 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 02 2009
EXTENSIONS
5 leading terms added. Conjecture clarified. - R. J. Mathar, Jul 07 2015
STATUS
approved