A211614 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>2.

0, 1, 11, 57, 160, 344, 633, 1051, 1622, 2370, 3319, 4493, 5916, 7612, 9605, 11919, 14578, 17606, 21027, 24865, 29144, 33888, 39121, 44867, 51150, 57994, 65423, 73461, 82132, 91460, 101469, 112183, 123626, 135822, 148795, 162569, 177168, 192616, 208937

Offset

0,3

Comments

For a guide to related sequences, see A211422.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

From Colin Barker, Dec 04 2017: (Start)

G.f.: x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4.

a(n) = (8*n^3 - 15*n^2 + 15*n - 12)/2 for n>1.

(End)

Mathematica

t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[w + x + y > 2, s = s + 1], {w, #}, {x, #}, {y, #}] &[ Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]]  (* A211614 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0, 1}, LinearRecurrence[{4, -6, 4, -1}, {11, 57, 160, 344}, 34]] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(0, Vec(x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017

Crossrefs

Cf. A211422.

Sequence in context: A114030 A071984 A323039 * A244497 A101094 A187693

Adjacent sequences: A211611 A211612 A211613 * A211615 A211616 A211617

Keyword

nonn,easy

Author

Clark Kimberling, Apr 16 2012

Status

approved