A212741 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>=2*min{w,x,y,z}.

1, 15, 79, 239, 593, 1199, 2239, 3759, 6049, 9119, 13391, 18815, 25969, 34719, 45823, 59039, 75329, 94319, 117199, 143439, 174481, 209615, 250559, 296399, 349153, 407679, 474319, 547679, 630449, 720959, 822271, 932415, 1054849, 1187279, 1333583, 1491119, 1664209, 1849839

Offset

0,2

Comments

Also the number of (w,x,y,z) with all terms in {0,...,n} and at least one term <= range{w,x,y,z}.

Every term is odd.

For a guide to related sequences, see A211795.

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

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.: (-1-13*x-47*x^2-57*x^3-47*x^4-3*x^5-x^6+x^7 )/((1+x)^3*(x-1)^5).

a(n) + A212740(n) = n^4.

From Stefano Spezia, Sep 04 2025: (Start)

a(n) = (15 + (-1)^n + 64*n + 6*(15 + (-1)^n)*n^2 + 64*n^3 + 14*n^4)/16.

E.g.f.: ((8+113 x+193 x^2+74 x^3+7 x^4) Cosh[x]+(7+119 x+187 x^2+74 x^3+7 x^4) Sinh[x])/8. (End)

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y, z] >= 2 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]]

Crossrefs

Cf. A211795, A212740, A212743.

Sequence in context: A044202 A044583 A212746 * A082540 A372952 A269657

Adjacent sequences: A212738 A212739 A212740 * A212742 A212743 A212744

Keyword

nonn,easy

Author

Clark Kimberling, May 26 2012

Status

approved