OFFSET
0,2
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 (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).
G.f.: (1+3*x+10*x^2-6*x^3-3*x^4+3*x^5) / ((1+x)^3*(x-1)^4).
From Colin Barker, Jan 29 2016: (Start)
a(n) = (2*n^3+3*((-1)^n+5)*n^2+(15*(-1)^n+37)*n+12)/12.
a(n) = (n^3+9*n^2+26*n+6)/6 for n even.
a(n) = (n^3+6*n^2+11*n+6)/6 for n odd. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == 2*Floor[(x + y + z)/2], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 45]] (* A212748 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 4, 17, 20, 53, 56, 117}, 50] (* Harvey P. Dale, Jun 08 2018 *)
PROG
(PARI) Vec((1+3*x+10*x^2-6*x^3-3*x^4+3*x^5)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 28 2012
STATUS
approved