A212750 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x=R, y<R, z<R, where R = max{w,x,y,z} - min{w,x,y,z}.

1, 14, 72, 216, 529, 1070, 1984, 3336, 5345, 8070, 11816, 16624, 22897, 30646, 40384, 52080, 66369, 83166, 103240, 126440, 153681, 184734, 220672, 261176, 307489, 359190, 417704, 482496, 555185, 635110, 724096, 821344, 928897

Offset

0,2

Comments

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).

G.f.:( -1-12*x-42*x^2-50*x^3-37*x^4-6*x^5 ) / ( (1+x)^3*(x-1)^5 ).

Mathematica

t = Compile[{{n, _Integer}},
Module[{s = 0}, (Do[
If[(w == # || x == # || y < # || z < #) &[
Max[w, x, y, z] - Min[w, x, y, z]], s++],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212750  *)
(* Peter J. C. Moses, May 24 2012 *)
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 14, 72, 216, 529, 1070, 1984, 3336}, 40] (* Harvey P. Dale, May 07 2022 *)

Crossrefs

Cf. A211795.

Sequence in context: A212752 A074086 A205335 * A106845 A365670 A205328

Adjacent sequences: A212747 A212748 A212749 * A212751 A212752 A212753

Keyword

nonn,easy

Author

Clark Kimberling, May 27 2012

Status

approved