A211435 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+4x+5y=0.

1, 3, 5, 11, 17, 25, 35, 45, 59, 73, 89, 107, 125, 147, 169, 193, 219, 245, 275, 305, 337, 371, 405, 443, 481, 521, 563, 605, 651, 697, 745, 795, 845, 899, 953, 1009, 1067, 1125, 1187, 1249, 1313, 1379, 1445, 1515, 1585, 1657, 1731, 1805, 1883

Offset: 0

Author

Clark Kimberling, Apr 11 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w + 4 x + 5 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211435 *)
(t - 1)/2                    (* integers *)

Formula

Conjectures from Colin Barker, May 15 2017: (Start)

G.f.: (1 + x + 4*x^3 + x^5 + x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).

a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n > 6. (End)

Conjecture: a(n) ~ 4*n^2/5. - Stefano Spezia, Oct 17 2022