A211533 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x-5y.

0, 0, 1, 1, 3, 4, 5, 8, 10, 13, 16, 19, 23, 27, 32, 36, 41, 47, 52, 59, 65, 71, 79, 86, 94, 102, 110, 119, 128, 138, 147, 157, 168, 178, 190, 201, 212, 225, 237, 250, 263, 276, 290, 304, 319, 333, 348, 364, 379, 396, 412, 428, 446, 463, 481, 499, 517, 536

Offset

0,5

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).

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^2*(1 + 2*x^2 + x^4 + x^6) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 02 2017

Mathematica

t[n_] := t[n] = Flatten[Table[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}]  (* A211533 *)
FindLinearRecurrence[t]
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {0, 0, 1, 1, 3, 4, 5, 8, 10}, 58] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(vector(2), Vec(x^2*(1 + 2*x^2 + x^4 + x^6) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 02 2017

Crossrefs

Cf. A211422.

Sequence in context: A028288 A118250 A278998 * A079136 A235862 A228305

Adjacent sequences: A211530 A211531 A211532 * A211534 A211535 A211536

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2012

Status

approved