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,-1,-5,5,1,-3,1).
FORMULA
a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).
From Colin Barker, Dec 06 2015: (Start)
a(n) = 1/48*(38*n^4+20*n^3-32*n^2-2*(3*(-1)^n-11)*n+3*((-1)^n-1)).
G.f.: x*(1+11*x+30*x^2+26*x^3+9*x^4-x^5) / ((1-x)^5*(1+x)^2).
(End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] <= Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212572 *)
PROG
(PARI) concat(0, Vec(x*(1+11*x+30*x^2+26*x^3+9*x^4-x^5)/((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 06 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 22 2012
STATUS
approved