A212511 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>=3z.

0, 0, 0, 7, 24, 57, 135, 259, 432, 732, 1125, 1638, 2376, 3302, 4410, 5915, 7680, 9765, 12393, 15447, 18900, 23170, 27951, 33348, 39744, 46900, 54756, 63999, 74088, 85185, 97875, 111755, 126720, 143792, 162129, 181962, 204120, 227994, 253422, 281827, 312000

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*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*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]]   (* A212511 *)

Prog

(PARI) concat(vector(3), Vec(x^3*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*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, A212509, A212510.

Sequence in context: A159225 A146298 A079671 * A100454 A081436 A024205

Adjacent sequences: A212508 A212509 A212510 * A212512 A212513 A212514

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved