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A212899 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>2. 3
0, 0, 0, 2, 16, 62, 186, 456, 962, 1818, 3162, 5156, 7986, 11862, 17018, 23712, 32226, 42866, 55962, 71868, 90962, 113646, 140346, 171512, 207618, 249162, 296666, 350676, 411762, 480518, 557562, 643536, 739106, 844962, 961818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The gapsizes are |w-x|, |x-y|, |y-z|.  Every term is even. a(n)+A212898(n)=(n+1)^4.

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..34.

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>=9.

G.f.: (2*x^3 + 6*x^4 + 2*x^5 + 16*x^6 - 4*x^7 + 2*x^9 )/(1 - 5*x + 10*x^2 - 10*x^3 + 5*x^4 - x^5)

MATHEMATICA

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

(Do[If[Min[Abs[w - x], Abs[x - y], Abs[y - z]] > 2, s = s + 1],

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

m = Map[t[#] &, Range[0, 40]]   (* A212899 *)

m/2  (* integers *)

CROSSREFS

Cf. A211795.

Sequence in context: A152665 A183762 A061608 * A127276 A076616 A222381

Adjacent sequences:  A212896 A212897 A212898 * A212900 A212901 A212902

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 31 2012

STATUS

approved

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Last modified October 17 13:20 EDT 2021. Contains 348049 sequences. (Running on oeis4.)