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A211628
Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 3w+x+y>0.
2
0, 4, 30, 105, 249, 487, 846, 1346, 2012, 2871, 3943, 5253, 6828, 8688, 10858, 13365, 16229, 19475, 23130, 27214, 31752, 36771, 42291, 48337, 54936, 62108, 69878, 78273, 87313, 97023, 107430, 118554, 130420, 143055, 156479, 170717, 185796, 201736, 218562
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n>5.
G.f.: x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Dec 05 2017
MATHEMATICA
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[3 w + x + y > 0,
s = s + 1], {w, #}, {x, #}, {y, #}] &[
Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211628 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 4, 30, 105, 249, 487}, 36] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Dec 05 2017
CROSSREFS
Cf. A211422.
Sequence in context: A328103 A211624 A027297 * A166761 A213824 A333277
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 17 2012
STATUS
approved