A212984 Number of (w,x,y) with all terms in {0..n} and 3w = x+y.

1, 1, 3, 6, 8, 12, 17, 21, 27, 34, 40, 48, 57, 65, 75, 86, 96, 108, 121, 133, 147, 162, 176, 192, 209, 225, 243, 262, 280, 300, 321, 341, 363, 386, 408, 432, 457, 481, 507, 534, 560, 588, 617, 645, 675, 706, 736, 768, 801, 833, 867, 902, 936, 972, 1009

Offset: 0

Author

Clark Kimberling, Jun 04 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Crossrefs

Cf. A212959.

Programs

Magma

[1 + Floor(2*n/3) + Floor(n^2/3) : n in [0..80]]; // Wesley Ivan Hurt, Jul 25 2016

Maple

A212984:=n->1 + floor(2*n/3) + floor(n^2/3): seq(A212984(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2016

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[3 w == x + y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 70]]   (* A212984 *)

Formula

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

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

a(n) = 1 + floor(2*n/3) + floor(n^2/3). - Wesley Ivan Hurt, Jul 25 2016