A212521 Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<=3z.

0, 0, 4, 18, 60, 138, 297, 528, 912, 1440, 2200, 3180, 4536, 6174, 8330, 10920, 14144, 17928, 22599, 27900, 34300, 41580, 50094, 59664, 70848, 83148, 97344, 113022, 130732, 150150, 172125, 195840, 222464, 251328, 283220, 317628, 355752, 396378, 441142

Offset

0,3

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^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((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]]   (* A212521 *)

Prog

(PARI) concat([0, 0], Vec(x^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((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: A119044 A058851 A167885 * A278406 A192069 A073373

Adjacent sequences: A212518 A212519 A212520 * A212522 A212523 A212524

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved