OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>4.
From Colin Barker, Dec 04 2017: (Start)
G.f.: x*(3 + 21*x + 17*x^2 + 7*x^3) / ((1 - x)^4*(1 + x)).
a(n) = 4*n^3 - n^2 + n for n even.
a(n) = 4*n^3 - n^2 + n - 1 for n odd.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[2 w + x + y > 0, s = s + 1], {w, #}, {x, #}, {y, #}] &[ Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]] (* A211617 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 3, 30, 101, 244}, 36] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(3 + 21*x + 17*x^2 + 7*x^3) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved