OFFSET
1,2
COMMENTS
Also, numbers of the form 9*m^2+6*m, m an integer. - Jason Kimberley, Nov 08 2012
k is in this list iff k+1 is in the support of A033684. - Jason Kimberley, Nov 13 2012
LINKS
Jason Kimberley, Table of n, a(n) for n = 1..2001
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f.: 3*x^2*(1+4*x+x^2) / ((1-x)^3*(1+x)^2). - Colin Barker, Nov 24 2012
From Colin Barker, Dec 26 2015: (Start)
a(n) = 3/8*(6*n^2-2*((-1)^n+3)*n+(-1)^n-1).
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.
(End)
MATHEMATICA
Select[3*Range[0, 2000], IntegerQ[Sqrt[#+1]]&] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 3, 15, 24, 48}, 50] (* Harvey P. Dale, Sep 10 2019 *)
PROG
(Magma) a:=func<n|9*n^2+6*n>; [0]cat[a(n*m):m in[-1, 1], n in[1..24]]; // Jason Kimberley, Nov 09 2012
(PARI) concat(0, Vec(3*x^2*(1+4*x+x^2)/((1-x)^3*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benjamin Geiger (benjamin_geiger(AT)yahoo.com), Nov 02 2000
EXTENSIONS
Since this is a list, offset corrected to 1 by Jason Kimberley, Nov 09 2012
STATUS
approved