A212566 Number of (w,x,y,z) with all terms in {1,...,n} and w+x=3y+3z.

0, 0, 0, 1, 3, 9, 16, 26, 44, 63, 87, 123, 160, 204, 264, 325, 395, 485, 576, 678, 804, 931, 1071, 1239, 1408, 1592, 1808, 2025, 2259, 2529, 2800, 3090, 3420, 3751, 4103, 4499, 4896, 5316, 5784, 6253, 6747, 7293, 7840, 8414, 9044, 9675, 10335, 11055, 11776

Offset: 0

Author

Clark Kimberling, May 21 2012

Keywords

• nonn
• easy

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 (2,-1,2,-4,2,-1,2,-1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x == 3 y + 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212566 *)

PARI

concat(vector(3), Vec(x^3*(1+x+4*x^2-x^3+x^4)/((1-x)^4*(1+x+x^2)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015

Formula

a(n) = 2 a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).

G.f.: x^3*(1+x+4*x^2-x^3+x^4) / ((1-x)^4*(1+x+x^2)^2). - Colin Barker, Dec 05 2015