OFFSET
0,3
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 (4,-6,4,-1).
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
From Colin Barker, Dec 04 2017: (Start)
G.f.: x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4.
a(n) = (8*n^3 - 15*n^2 + 15*n - 12)/2 for n>1.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[w + x + y > 2, s = s + 1], {w, #}, {x, #}, {y, #}] &[ Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211614 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0, 1}, LinearRecurrence[{4, -6, 4, -1}, {11, 57, 160, 344}, 34]] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved