A212982 Number of (w,x,y) with all terms in {0,...,n} and w

0, 3, 11, 27, 53, 92, 146, 218, 310, 425, 565, 733, 931, 1162, 1428, 1732, 2076, 2463, 2895, 3375, 3905, 4488, 5126, 5822, 6578, 7397, 8281, 9233, 10255, 11350, 12520, 13768, 15096, 16507, 18003, 19587, 21261, 23028, 24890, 26850, 28910, 31073, 33341, 35717

Offset: 0

Author

Clark Kimberling, Jun 04 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < x + y && x <= y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212982 *)

PARI

concat(0, Vec(x*(3+2*x)/((1-x)^4*(1+x)) + O(x^100))) \\ Colin Barker, Jan 28 2016

Formula

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

G.f.: f(x)/g(x), where f(x)=3*x + 2*x^2 and g(x)=(1+x)*(1-x)^4.

From Colin Barker, Jan 28 2016: (Start)

a(n) = (20*n^3+66*n^2+52*n-3*(-1)^n+3)/48.

a(n) = (10*n^3+33*n^2+26*n)/24 for n even.

a(n) = (10*n^3+33*n^2+26*n+3)/24 for n odd.

(End)