|
|
A211612
|
|
Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>=0.
|
|
2
|
|
|
0, 4, 35, 117, 274, 530, 909, 1435, 2132, 3024, 4135, 5489, 7110, 9022, 11249, 13815, 16744, 20060, 23787, 27949, 32570, 37674, 43285, 49427, 56124, 63400, 71279, 79785, 88942, 98774, 109305, 120559, 132560, 145332, 158899, 173285, 188514, 204610, 221597
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
For a guide to related sequences, see A211422.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x*(4 + 19*x + x^2) / (1 - x)^4.
a(n) = (n*(-3 + 3*n + 8*n^2))/2.
(End)
|
|
MATHEMATICA
|
t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[w + x + y >= 0, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211612 *)
FindLinearRecurrence[%]
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 35, 117}, 36] (* Ray Chandler, Aug 02 2015 *)
|
|
PROG
|
(PARI) concat(0, Vec(x*(4 + 19*x + x^2) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|