OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
LINKS
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).
G.f.: (1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^4*(1 + x + x^2)).
a(n) = (n+1)^3 - A213396(n).
a(n) = floor(2*n^3/3) + 2*n*(n + 1) + 1. - Bruno Berselli, Dec 22 2017
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w >= Abs[x + y - w], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A212297 *)
CoefficientList[Series[(1 + 2 x + 6 x^2 + 2 x^3 + x^4)/((1 - x)^4*(1 + x + x^2)), {x, 0, 44}], x] (* Michael De Vlieger, Dec 22 2017 *)
PROG
(PARI) first(n) = Vec((1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^4*(1 + x + x^2)) + O(x^n)) \\ Iain Fox, Dec 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 12 2012
STATUS
approved