A211544 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x-5y.

0, 0, 0, 1, 2, 3, 4, 5, 8, 10, 12, 15, 17, 21, 25, 28, 32, 36, 41, 46, 51, 56, 61, 68, 74, 80, 87, 93, 101, 109, 116, 124, 132, 141, 150, 159, 168, 177, 188, 198, 208, 219, 229, 241, 253, 264, 276, 288, 301, 314, 327, 340, 353, 368, 382, 396, 411, 425, 441

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

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[2 w - 3 x + 5 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]   (* A211544 *)
FindLinearRecurrence[t]
LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{0,0,0,0,1,1,1,2,3},63] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(vector(3), Vec(x^3*(1 + x)*(1 + x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 03 2017

Formula

a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) - a(n-6) - a(n-8) + a(n-9).

G.f.: x^3*(1 + x)*(1 + x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) - Colin Barker, Dec 03 2017