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
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) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>=9.
G.f.: f(x)/g(x), where f(x)=(2 x^2)*(1 + 3 x + 7 x^2 + 6 x^3 - x^4 + x^5 + x^6) 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]] == 2, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 40]] (* A212895 *)
m/2 (* integers *)
CoefficientList[Series[2 x^2*(1+3 x+7 x^2+6 x^3-x^4+x^5+x^6) /(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)
PROG
(Magma) I:=[0, 0, 2, 14, 58, 168, 376, 716, 1224]; [n le 9 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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 31 2012
STATUS
approved