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A211620
Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -1<=2w+x+y<=1.
2
0, 2, 16, 38, 76, 122, 184, 254, 340, 434, 544, 662, 796, 938, 1096, 1262, 1444, 1634, 1840, 2054, 2284, 2522, 2776, 3038, 3316, 3602, 3904, 4214, 4540, 4874, 5224, 5582, 5956, 6338, 6736, 7142, 7564, 7994, 8440, 8894, 9364, 9842, 10336, 10838, 11356, 11882
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
FORMULA
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
From Colin Barker, Dec 04 2017: (Start)
G.f.: 2*x*(1 + 6*x + 3*x^2 + 2*x^3) / ((1 - x)^3*(1 + x)).
a(n) = 6*n^2 - 6*n + 4 for n>0 and even.
a(n) = 6*n^2 - 6*n + 2 for n odd.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[-1 <= 2 w + x + y <= 1,
s = s + 1], {w, #}, {x, #}, {y, #}] &[
Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]] (* A211620 *)
%/2 (* integers *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0}, LinearRecurrence[{2, 0, -2, 1}, {2, 16, 38, 76}, 42]] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(2*x*(1 + 6*x + 3*x^2 + 2*x^3) / ((1 - x)^3*(1 + x)) + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
Cf. A211422.
Sequence in context: A327542 A166154 A034507 * A023638 A139267 A254855
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved