|
|
A212566
|
|
Number of (w,x,y,z) with all terms in {1,...,n} and w+x=3y+3z.
|
|
2
|
|
|
0, 0, 0, 1, 3, 9, 16, 26, 44, 63, 87, 123, 160, 204, 264, 325, 395, 485, 576, 678, 804, 931, 1071, 1239, 1408, 1592, 1808, 2025, 2259, 2529, 2800, 3090, 3420, 3751, 4103, 4499, 4896, 5316, 5784, 6253, 6747, 7293, 7840, 8414, 9044, 9675, 10335, 11055, 11776
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
For a guide to related sequences, see A211795.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2 a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
G.f.: x^3*(1+x+4*x^2-x^3+x^4) / ((1-x)^4*(1+x+x^2)^2). - Colin Barker, Dec 05 2015
|
|
MATHEMATICA
|
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x == 3 y + 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212566 *)
|
|
PROG
|
(PARI) concat(vector(3), Vec(x^3*(1+x+4*x^2-x^3+x^4)/((1-x)^4*(1+x+x^2)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|