A212517 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y<=3z.

0, 0, 0, 9, 30, 92, 198, 396, 684, 1152, 1760, 2650, 3780, 5292, 7140, 9555, 12376, 15936, 20088, 25110, 30870, 37800, 45540, 54692, 64944, 76752, 89856, 104949, 121394, 140140, 160650, 183600, 208560, 236544, 266560, 299982, 335988, 375516, 417924, 464607

Offset

0,4

Comments

For a guide to related sequences, see A211795.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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^3*(9 +30*x +74*x^2 +120*x^3 +161*x^4 +170*x^5 +176*x^6 +148*x^7 +106*x^8 +58*x^9 +24*x^10 +4*x^11) / ((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]]   (* A212517 *)
FindLinearRecurrence[%]
LinearRecurrence[{0, 2, 2, -1, -4, 0, 2, 0, -2, 0, 4, 1, -2, -2, 0, 1}, {0, 0, 0, 9, 30, 92, 198, 396, 684, 1152, 1760, 2650, 3780, 5292, 7140, 9555}, 37] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(vector(3), Vec(x^3*(9 +30*x +74*x^2 +120*x^3 +161*x^4 +170*x^5 +176*x^6 +148*x^7 +106*x^8 +58*x^9 +24*x^10 +4*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Crossrefs

Cf. A211795, A212508.

Sequence in context: A291919 A301988 A334853 * A319839 A274998 A000440

Adjacent sequences: A212514 A212515 A212516 * A212518 A212519 A212520

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved