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,-3,2,-3,3,-1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n>5.
G.f.: x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Dec 05 2017
MATHEMATICA
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[3 w + x + y > 0,
s = s + 1], {w, #}, {x, #}, {y, #}] &[
Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211628 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 4, 30, 105, 249, 487}, 36] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Dec 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 17 2012
STATUS
approved