A212894 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)=1.

0, 2, 22, 92, 246, 520, 950, 1572, 2422, 3536, 4950, 6700, 8822, 11352, 14326, 17780, 21750, 26272, 31382, 37116, 43510, 50600, 58422, 67012, 76406, 86640, 97750, 109772, 122742, 136696, 151670, 167700, 184822, 203072, 222486, 243100

Offset

0,2

Comments

The gapsizes are |w-x|, |x-y|, |y-z|. Every term is even. For a guide to related sequences, see A211795.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 2*(n-1)*(3*n^2-3*n+5) with n>1, a(0)=0, a(1)=2.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>=6.

G.f.: f(x)/g(x), where f(x)=2*(x+7*x^2+8*x^3+x^4+x^5) and g(x)=(1-x)^4.

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]]   (* A212894 *)
m/2 (* integers *)
CoefficientList[Series[2*(x+7*x^2+8*x^3+x^4+x^5) /(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)

Prog

(Magma) I:=[0, 2, 22, 92, 246, 520]; [n le 6 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 04 2012 *)

Crossrefs

Cf. A211795.

Sequence in context: A050853 A291915 A172229 * A281647 A344498 A281140

Adjacent sequences: A212891 A212892 A212893 * A212895 A212896 A212897

Keyword

nonn,easy

Author

Clark Kimberling, May 30 2012

Status

approved