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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

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.

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