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A212896
Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)<2.
2
1, 16, 79, 240, 551, 1066, 1839, 2924, 4375, 6246, 8591, 11464, 14919, 19010, 23791, 29316, 35639, 42814, 50895, 59936, 69991, 81114, 93359, 106780, 121431, 137366, 154639, 173304, 193415, 215026, 238191, 262964, 289399, 317550
OFFSET
0,2
COMMENTS
The gapsizes are |w-x|, |x-y|, |y-z|.
For a guide to related sequences, see A211795.
FORMULA
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) = 1+12*x+21*x^2+16*x^3+2*x^4+2*x^5 and g(x) = (1-x)^4.
a(n) = 9*n^3-6*n^2+20*n-9 with n>1, a(0)=1, a(1)=16. [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]] (* A212896 *)
CoefficientList[Series[(1+12*x+21*x^2+16*x^3+2*x^4+2*x^5) /(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)
PROG
(Magma) I:=[1, 16, 79, 240, 551, 1066]; [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 20123
CROSSREFS
Cf. A211795.
Sequence in context: A212563 A210324 A250231 * A250279 A269584 A373927
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 31 2012
STATUS
approved