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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: A195960 A268684 A075036 * A091405 A085929 A231247

Adjacent sequences:  A212899 A212900 A212901 * A212903 A212904 A212905

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 01 2012

STATUS

approved

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Last modified July 24 02:42 EDT 2019. Contains 325287 sequences. (Running on oeis4.)