OFFSET
1,1
COMMENTS
For no term n of the sequence, 36*n^2+72*n+35 = (6*n+5)*(6*n+7) is of the form p*(p+2), where p and p+2 are 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) = (74*n+13*(-1)^n -41)/4 . - Bruno Berselli, Jan 05 2013
G.f.: x*(5+25*x+7*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015
MATHEMATICA
Select[Range[1, 1200], MemberQ[{5, 30}, Mod[#, 37]]&] (* Harvey P. Dale, Sep 07 2012 *)
LinearRecurrence[{1, 1, -1}, {5, 30, 42}, 57] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(5+25*x+7*x^2)/((1+x)*(x-1)^2), {x, 0, 57}], x]] (* Ray Chandler, Jul 08 2015 *)
PROG
(Magma) I:=[5, 30 , 42]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Jan 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 03 2009
EXTENSIONS
Added missing terms. Clarified the comment. - R. J. Mathar, Jul 07 2015
STATUS
approved