The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A211612 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>=0. 2
0, 4, 35, 117, 274, 530, 909, 1435, 2132, 3024, 4135, 5489, 7110, 9022, 11249, 13815, 16744, 20060, 23787, 27949, 32570, 37674, 43285, 49427, 56124, 63400, 71279, 79785, 88942, 98774, 109305, 120559, 132560, 145332, 158899, 173285, 188514, 204610, 221597 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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).
From Colin Barker, Dec 04 2017: (Start)
G.f.: x*(4 + 19*x + x^2) / (1 - x)^4.
a(n) = (n*(-3 + 3*n + 8*n^2))/2.
(End)
MATHEMATICA
t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[w + x + y >= 0, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211612 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 35, 117}, 36] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(4 + 19*x + x^2) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017
CROSSREFS
Cf. A211422.
Sequence in context: A344642 A297546 A257600 * A068968 A228887 A185592
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 14 01:49 EDT 2024. Contains 373391 sequences. (Running on oeis4.)