A213392 Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) >= 3*min(w,x,y).

1, 7, 25, 61, 115, 199, 319, 469, 667, 919, 1213, 1573, 2005, 2491, 3061, 3721, 4447, 5275, 6211, 7225, 8359, 9619, 10969, 12457, 14089, 15823, 17713, 19765, 21931, 24271, 26791, 29437, 32275, 35311, 38485, 41869, 45469, 49219, 53197

Offset

0,2

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Formula

a(n) + A213391(n) = (n+1)^3.

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.: -(-1 - 5*x - x^6 - 12*x^2 - 16*x^3 - 8*x^4 - 6*x^5 + x^7) / ((x^2 + x + 1)^2*(x-1)^4).

From Ayoub Saber Rguez, Feb 01 2022: (Start)

a(n) = A213393(n) + A092076(n).

a(n) = (8*n^3 + 27*n^2 + 21*n + 6*n*(((n+1) mod 3) mod 2) + 7 + 2*((2*n+1) mod 3))/9. (End)

From Jon E. Schoenfield, Feb 02 2022: (Start)

a(n) = (8*n^3 + 27*n^2 + 27*n + 9)/9 if n == 0 (mod 3);

= (8*n^3 + 27*n^2 + 21*n + 7)/9 if n == 1 (mod 3);

= (8*n^3 + 27*n^2 + 21*n + 11)/9 if n == 2 (mod 3).

(End)

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2*Max[w, x, y] >= 3*Min[w, x, y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 45]]   (* A213391 *)

Crossrefs

Cf. A212959, A213391.

Sequence in context: A162264 A034135 A212136 * A061600 A098538 A033814

Adjacent sequences: A213389 A213390 A213391 * A213393 A213394 A213395

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2012

Status

approved