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A212897 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>1. 2
0, 0, 2, 16, 74, 230, 562, 1172, 2186, 3754, 6050, 9272, 13642, 19406, 26834, 36220, 47882, 62162, 79426, 100064, 124490, 153142, 186482, 224996, 269194, 319610, 376802, 441352, 513866, 594974, 685330, 785612, 896522, 1018786 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The gapsizes 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..33.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>=7.

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

a(n) = n^4-5*n^3+12*n^2-16*n+10 with n>1, a(0)=a(1)=0. [Bruno Berselli, Jun 12 2012]

MATHEMATICA

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

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

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

m = Map[t[#] &, Range[0, 40]]   (* A212897 *)

m/2 (* integers *)

CROSSREFS

Cf. A211795.

Sequence in context: A207923 A207839 A216424 * A289837 A323297 A034581

Adjacent sequences:  A212894 A212895 A212896 * A212898 A212899 A212900

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.)