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A212514
Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>3z.
2
0, 0, 0, 0, 14, 42, 90, 200, 364, 585, 960, 1440, 2052, 2926, 4004, 5280, 7000, 9000, 11340, 14280, 17670, 21483, 26180, 31416, 37296, 44252, 52000, 60480, 70434, 81270, 93150, 106720, 121520, 137445, 155584, 175032, 196020, 219450, 244644, 271440, 301340
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*(14 +42*x +62*x^2 +88*x^3 +114*x^4 +103*x^5 +90*x^6 +74*x^7 +42*x^8 +15*x^9 +4*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 18 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]] (* A212514 *)
LinearRecurrence[{0, 2, 2, -1, -4, 0, 2, 0, -2, 0, 4, 1, -2, -2, 0, 1}, {0, 0, 0, 0, 14, 42, 90, 200, 364, 585, 960, 1440, 2052, 2926, 4004, 5280}, 50] (* Harvey P. Dale, Dec 24 2020 *)
PROG
(PARI) concat(vector(4), Vec(x^4*(14 +42*x +62*x^2 +88*x^3 +114*x^4 +103*x^5 +90*x^6 +74*x^7 +42*x^8 +15*x^9 +4*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^60))) \\ Colin Barker, Dec 18 2015
CROSSREFS
Sequence in context: A163756 A005587 A244101 * A292051 A242897 A120714
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 20 2012
STATUS
approved