login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211613 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>1. 2
0, 1, 20, 78, 199, 407, 726, 1180, 1793, 2589, 3592, 4826, 6315, 8083, 10154, 12552, 15301, 18425, 21948, 25894, 30287, 35151, 40510, 46388, 52809, 59797, 67376, 75570, 84403, 93899, 104082, 114976, 126605, 138993, 152164, 166142, 180951, 196615, 213158 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211422.
LINKS
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
From Colin Barker, Dec 04 2017: (Start)
G.f.: x*(1 + 16*x + 4*x^2 + 3*x^3) / (1 - x)^4.
a(n) = (-6 + 9*n - 9*n^2 + 8*n^3)/2 for n>0.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[w + x + y > 1, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211613 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0}, LinearRecurrence[{4, -6, 4, -1}, {1, 20, 78, 199}, 35]] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(1 + 16*x + 4*x^2 + 3*x^3) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
Cf. A211422.
Sequence in context: A219941 A266133 A083127 * A292360 A337988 A002609
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 21:17 EDT 2024. Contains 373609 sequences. (Running on oeis4.)