OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4, 1).
FORMULA
a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
a(n) = (3-3*(-1)^n-8*n-4*n^2+8*n^3+94*n^4)/96. - Colin Barker, Nov 21 2014
G.f.: -x*(x^4+11*x^3+22*x^2+12*x+1) / ((x-1)^5*(x+1)). - Colin Barker, Nov 21 2014
MAPLE
A212145:=n->(3-3*(-1)^n-8*n-4*n^2+8*n^3+94*n^4)/96: seq(A212145(n), n=0..40); # Wesley Ivan Hurt, Nov 21 2014
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < 2 x + y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]] (* A212145 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
CoefficientList[Series[x (x^4 + 11 x^3 + 22 x^2 + 12 x + 1) / ((1 - x)^5 (x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 16, 81, 255, 621}, 34] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(-x*(x^4+11*x^3+22*x^2+12*x+1)/((x-1)^5*(x+1)) + O(x^100))) \\ Colin Barker, Nov 21 2014
(Magma) [(3-3*(-1)^n-8*n-4*n^2+8*n^3+94*n^4)/96 : n in [0..40]]; // Wesley Ivan Hurt, Nov 21 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 02 2012
STATUS
approved