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A212517 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y<=3z. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A002414 A273604 A273640 * A274998 A000440 A161684

Adjacent sequences:  A212514 A212515 A212516 * A212518 A212519 A212520

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 20 2012

STATUS

approved

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Last modified December 6 15:25 EST 2016. Contains 278781 sequences.