A212744 Number of (w,x,y,z) with all terms in {0,...,n} and w=max{w,x,y,z}-min{w,x,y,z}; i.e., the range of (w,x,y,z) is its first term.

1, 8, 34, 83, 181, 314, 532, 791, 1177, 1604, 2206, 2843, 3709, 4598, 5776, 6959, 8497, 10016, 11962, 13859, 16261, 18578, 21484, 24263, 27721, 31004, 35062, 38891, 43597, 48014, 53416, 58463, 64609, 70328, 77266, 83699, 91477, 98666, 107332, 115319, 124921

Offset

0,2

Comments

For a guide to related sequences, see A211795.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1)

Formula

a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).

G.f.: (1+x+x^2)*(x^4+6*x^3+16*x^2+6*x+1) / ((1+x)^3*(x-1)^4).

From Colin Barker, Jan 28 2016: (Start)

a(n) = (30*n^3+3*((-1)^n+15)*n^2+3*((-1)^n+15)*n+(-1)^n+15)/16.

a(n) = (15*n^3+24*n^2+24*n+8)/8 for n even.

a(n) = (15*n^3+21*n^2+21*n+7)/8 for n odd.

(End)

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == Max[w, x, y, z] - Min[w, x, y, z],
  s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212744 *)

Prog

(PARI) Vec((1+x+x^2)*(x^4+6*x^3+16*x^2+6*x+1)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 28 2016

Crossrefs

Cf. A211795.

Sequence in context: A307091 A024847 A154516 * A298174 A249743 A298140

Adjacent sequences: A212741 A212742 A212743 * A212745 A212746 A212747

Keyword

nonn,easy

Author

Clark Kimberling, May 26 2012

Status

approved