A212518 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>3z.

0, 0, 0, 0, 2, 8, 18, 45, 84, 144, 240, 375, 540, 792, 1092, 1470, 1960, 2560, 3240, 4131, 5130, 6300, 7700, 9317, 11088, 13248, 15600, 18252, 21294, 24696, 28350, 32625, 37200, 42240, 47872, 54043, 60588, 68040, 75924, 84474, 93860, 104000, 114660, 126567

Offset

0,5

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^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +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]]   (* A212518 *)

Prog

(PARI) concat(vector(4), Vec(x^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +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: A220909 A058858 A236633 * A264054 A073307 A064009

Adjacent sequences: A212515 A212516 A212517 * A212519 A212520 A212521

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved