A211522 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w + 5y = 2x.

0, 0, 0, 1, 2, 3, 4, 6, 8, 11, 13, 16, 19, 23, 27, 31, 35, 40, 45, 51, 56, 62, 68, 75, 82, 89, 96, 104, 112, 121, 129, 138, 147, 157, 167, 177, 187, 198, 209, 221, 232, 244, 256, 269, 282, 295, 308, 322, 336, 351, 365, 380, 395, 411, 427, 443, 459, 476

Offset: 0

Author

Clark Kimberling, Apr 14 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 (1,1,-1,0,1,-1,-1,1).

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w - 2 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}]  (* A211522 *)
FindLinearRecurrence[t]
LinearRecurrence[{1,1,-1,0,1,-1,-1,1},{0,0,0,1,2,3,4,6},58] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(vector(3), Vec(x^3*(1 + x + x^4) / ((1 - x)^3*(1 + x)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 02 2017

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) - a(n-6) - a(n-7) + a(n-8).

G.f.: x^3*(1 + x + x^4) / ((1 - x)^3*(1 + x)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 02 2017

a(n) ~ 3*n^2/20. - Stefano Spezia, Mar 11 2025