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A211616
Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -2<=w+x+y<=2.
2
0, 6, 42, 102, 192, 312, 462, 642, 852, 1092, 1362, 1662, 1992, 2352, 2742, 3162, 3612, 4092, 4602, 5142, 5712, 6312, 6942, 7602, 8292, 9012, 9762, 10542, 11352, 12192, 13062, 13962, 14892, 15852, 16842, 17862, 18912, 19992, 21102, 22242, 23412, 24612, 25842
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
From Colin Barker, Dec 04 2017: (Start)
G.f.: 6*x*(1 + 4*x - x^2 + x^3) / (1 - x)^3.
a(n) = 3*(4 - 5*n + 5*n^2) for n>1.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[-2 <= w + x + y <= 2, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]] (* A211616 *)
%/6 (* integers *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0, 6}, LinearRecurrence[{3, -3, 1}, {42, 102, 192}, 38]] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(6*x*(1 + 4*x - x^2 + x^3) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
Cf. A211422.
Sequence in context: A191764 A043896 A044489 * A153786 A256833 A164016
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved