A212987 Number of (w,x,y) with all terms in {0,...,n} and 3*w = 2*x+2*y.

1, 1, 3, 5, 8, 10, 16, 18, 25, 29, 37, 41, 52, 56, 68, 74, 87, 93, 109, 115, 132, 140, 158, 166, 187, 195, 217, 227, 250, 260, 286, 296, 323, 335, 363, 375, 406, 418, 450, 464, 497, 511, 547, 561, 598, 614, 652, 668, 709, 725, 767, 785, 828, 846, 892

Offset

0,3

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..54.

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

Formula

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

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

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[3 w == 2 x + 2 y, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 70]]   (* A212987 *)

Crossrefs

Cf. A212959.

Sequence in context: A310025 A133097 A117176 * A217919 A127700 A101907

Adjacent sequences: A212984 A212985 A212986 * A212988 A212989 A212990

Keyword

nonn,easy

Author

Clark Kimberling, Jun 04 2012

Status

approved