

A212681


Number of (w,x,y,z) with all terms in {1,...,n} and xy<yz.


2



0, 0, 4, 24, 88, 230, 504, 966, 1696, 2772, 4300, 6380, 9144, 12714, 17248, 22890, 29824, 38216, 48276, 60192, 74200, 90510, 109384, 131054, 155808, 183900, 215644, 251316, 291256, 335762, 385200, 439890, 500224, 566544, 639268
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OFFSET

0,3


COMMENTS

Also, the number of (w,x,y,z) with all terms in {1,...,n} and xy>yz. a(n)+A212682(n)=n^4. Every term is even.
For a guide to related sequences, see A211795.


LINKS

Table of n, a(n) for n=0..34.
Index entries for linear recurrences with constant coefficients, signature (3,1,5,5,1,3,1).


FORMULA

a(n) = 3*a(n1)a(n2)5*a(n3)+5*a(n4)+a(n5)3*a(n6)+a(n7).
G.f.: (4*x^2 + 12*x^3 + 20*x^4 + 10*x^5 + 2*x^6)/(1  3*x + x^2 + 5*x^3  5*x^4  x^5 + 3*x^6  x^7).


MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[x  y] < Abs[y  z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212681 *)
%/2 (* integers *)
LinearRecurrence[{3, 1, 5, 5, 1, 3, 1}, {0, 0, 4, 24, 88, 230, 504}, 40]


CROSSREFS

Cf. A211795.
Sequence in context: A005561 A061612 A097875 * A026694 A026967 A026977
Adjacent sequences: A212678 A212679 A212680 * A212682 A212683 A212684


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, May 24 2012


STATUS

approved



