A212985 Number of (w,x,y) with all terms in {0,...,n} and 3w = 3x + y.

1, 2, 3, 7, 9, 11, 18, 21, 24, 34, 38, 42, 55, 60, 65, 81, 87, 93, 112, 119, 126, 148, 156, 164, 189, 198, 207, 235, 245, 255, 286, 297, 308, 342, 354, 366, 403, 416, 429, 469, 483, 497, 540, 555, 570, 616, 632, 648, 697, 714, 731, 783, 801, 819, 874

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 (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[3 w == 3 x + y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 70]]   (* A212985 *)

Formula

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

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