OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
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).
G.f.: f(x)/g(x), where f(x)=3*x + 2*x^2 and g(x)=(1+x)*(1-x)^4.
From Colin Barker, Jan 28 2016: (Start)
a(n) = (20*n^3+66*n^2+52*n-3*(-1)^n+3)/48.
a(n) = (10*n^3+33*n^2+26*n)/24 for n even.
a(n) = (10*n^3+33*n^2+26*n+3)/24 for n odd.
(End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < x + y && x <= y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A212982 *)
PROG
(PARI) concat(0, Vec(x*(3+2*x)/((1-x)^4*(1+x)) + O(x^100))) \\ Colin Barker, Jan 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 04 2012
STATUS
approved