|
|
A212522
|
|
Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y>3z.
|
|
2
|
|
|
0, 0, 0, 0, 4, 12, 27, 60, 112, 180, 300, 450, 648, 924, 1274, 1680, 2240, 2880, 3645, 4590, 5700, 6930, 8470, 10164, 12096, 14352, 16900, 19656, 22932, 26460, 30375, 34800, 39680, 44880, 50864, 57222, 64152, 71820, 80142, 88920, 98800, 109200, 120393
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
For a guide to related sequences, see A211795.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).
|
|
FORMULA
|
a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^4*(4 +12*x +19*x^2 +28*x^3 +38*x^4 +34*x^5 +31*x^6 +26*x^7 +16*x^8 +6*x^9 +2*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015
|
|
MATHEMATICA
|
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= 2 x && y > 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212522 *)
|
|
PROG
|
(PARI) concat(vector(4), Vec(x^4*(4 +12*x +19*x^2 +28*x^3 +38*x^4 +34*x^5 +31*x^6 +26*x^7 +16*x^8 +6*x^9 +2*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|