A212515 Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>=3z.

0, 0, 0, 8, 28, 63, 150, 280, 468, 780, 1200, 1728, 2508, 3458, 4620, 6160, 8000, 10125, 12852, 15960, 19530, 23870, 28798, 34272, 40848, 48100, 56160, 65520, 75852, 87075, 100050, 114080, 129360, 146608, 165308, 185328, 207900, 231990, 257868, 286520

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*(8 +28*x +47*x^2 +78*x^3 +106*x^4 +102*x^5 +95*x^6 +90*x^7 +56*x^8 +26*x^9 +10*x^10 +2*x^11) / ((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]]   (* A212515 *)

Prog

(PARI) concat(vector(3), Vec(x^3*(8 +28*x +47*x^2 +78*x^3 +106*x^4 +102*x^5 +95*x^6 +90*x^7 +56*x^8 +26*x^9 +10*x^10 +2*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^60))) \\ Colin Barker, Dec 18 2015

Crossrefs

Cf. A211795, A212508.

Sequence in context: A264354 A033580 A299289 * A342251 A007331 A002408

Adjacent sequences: A212512 A212513 A212514 * A212516 A212517 A212518

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved