OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
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).
From Colin Barker, Dec 02 2017: (Start)
G.f.: x^2*(3 + x + x^2) / ((1 - x)^4*(1 + x)).
a(n) = n*(10*n^2 - 3*n + 2)/24 for n even.
a(n) = (n - 1)*(10*n^2 + 7*n + 9)/24 for n odd.
(End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w == x + y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212068 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 3, 10, 25}, 42] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(vector(2), Vec(x^2*(3 + x + x^2) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ Colin Barker, Dec 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 01 2012
STATUS
approved