login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212902 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<|x-y|<|y-z|. 2
0, 0, 2, 14, 44, 110, 228, 426, 726, 1168, 1780, 2612, 3700, 5104, 6866, 9058, 11728, 14958, 18804, 23358, 28682, 34880, 42020, 50216, 59544, 70128, 82050, 95446, 110404, 127070, 145540, 165970, 188462, 213184, 240244, 269820, 302028 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Every term is even.

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).

FORMULA

a(n) = 2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-a(n-7)-2*a(n-8)+a(n-9).

G.f.: (2*x^2 + 10*x^3 + 14*x^4 + 14*x^5 + 8*x^6 + 4*x^7 )/(1 - 2*x - x^2 + 3*x^3 + x^4 - x^5 - 3*x^6 + x^7 + 2*x^8 - x^9).

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[Abs[w - x] < Abs[x - y] < Abs[y - z], s = s + 1],

{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];

m = Map[t[#] &, Range[0, 40]]   (* A212902 *)

m/2 (* integers *)

LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 0, 2, 14, 44, 110, 228, 426, 726}, 40]

CROSSREFS

Cf. A211795.

Sequence in context: A268684 A333052 A075036 * A091405 A085929 A231247

Adjacent sequences:  A212899 A212900 A212901 * A212903 A212904 A212905

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 01 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 11:30 EST 2021. Contains 349429 sequences. (Running on oeis4.)