A212986 Number of (w,x,y) with all terms in {0,...,n} and 2w = 3x+y.

1, 1, 3, 5, 7, 10, 14, 17, 22, 27, 32, 38, 45, 51, 59, 67, 75, 84, 94, 103, 114, 125, 136, 148, 161, 173, 187, 201, 215, 230, 246, 261, 278, 295, 312, 330, 349, 367, 387, 407, 427, 448, 470, 491, 514, 537, 560, 584, 609, 633, 659, 685, 711, 738, 766

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

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[2 w == 3 x + y, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 70]]   (* A212986 *)

Formula

a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6).

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