A211535 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=4x+5y.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 23, 24, 25, 27, 29, 31, 32, 34, 36, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 60, 63, 65, 67, 70, 73, 76, 78, 81, 84, 87, 90, 93, 96, 99, 102, 106, 109

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

Crossrefs

Cf. A211422, A205772.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[-w + 4 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}]  (* A211535 *)
FindLinearRecurrence[t]
LinearRecurrence[{1,0,0,1,0,-1,0,0,-1,1},{0,0,0,0,0,0,0,0,0,1},71] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(vector(9), Vec(x^9 / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Colin Barker, Dec 03 2017

Formula

a(n) = a(n-1) + a(n-4) - a(n-6) - a(n-9) + a(n-10).

G.f.: x^9 / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 03 2017

a(n)-a(n-1)=A165190(n-9). - R. J. Mathar, Jun 23 2021