A211546 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x-3y.

0, 0, 0, 2, 3, 4, 9, 11, 13, 21, 24, 27, 38, 42, 46, 60, 65, 70, 87, 93, 99, 119, 126, 133, 156, 164, 172, 198, 207, 216, 245, 255, 265, 297, 308, 319, 354, 366, 378, 416, 429, 442, 483, 497, 511, 555, 570, 585, 632, 648, 664, 714, 731, 748, 801, 819

Offset: 0

Author

Clark Kimberling, Apr 15 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211422.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w - 3 x + 3 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211546 *)
FindLinearRecurrence[t]
LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,2,3,4,9},56] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(vector(3), Vec(x^3*(2 + x + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^40))) \\ Colin Barker, Dec 03 2017

Formula

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

G.f.: x^3*(2 + x + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2)^2). - Colin Barker, Dec 03 2017