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A212900 Number of (w,x,y,z) with all terms in {0,...,n} and distinct consecutive gap sizes. 3
0, 4, 28, 122, 340, 786, 1558, 2814, 4690, 7404, 11130, 16140, 22652, 30992, 41416, 54310, 69968, 88830, 111234, 137674, 168526, 204344, 245542, 292728, 346360, 407100, 475444, 552114, 637644, 732810, 838190, 954614, 1082698 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The gap sizes are |w-x|, |x-y|, |y-z|.  Every term is even.

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..32.

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.: f(x)/g(x), where f(x) = 2(2*x + 10*x^2 + 31*x^3 + 40*x^4 + 36*x^5 + 18*x^6 + 7*x^7) and g(x)=((1-x)^5)((1+x)^2)(1+x+x^2).

EXAMPLE

a(1)=4 counts these (w,x,y,z): (0,0,1,1), (0,1,1,0), (1,1,0,0), (1,0,0,1).

MATHEMATICA

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

(Do[If[Abs[w - x] != Abs[x - y] && 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]]   (* A212900 *)

m/2  (* integers *)

LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 4, 28, 122, 340, 786, 1558, 2814, 4690}, 40] (* Harvey P. Dale, Aug 25 2013 *)

CROSSREFS

Cf. A211795.

Sequence in context: A296392 A318011 A328685 * A196514 A249629 A131459

Adjacent sequences:  A212897 A212898 A212899 * A212901 A212902 A212903

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 31 2012

STATUS

approved

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Last modified November 28 04:31 EST 2021. Contains 349400 sequences. (Running on oeis4.)