A211524 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x+5y.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 20, 22, 23, 25, 27, 29, 31, 33, 35, 37, 40, 42, 44, 47, 49, 52, 55, 57, 60, 63, 66, 69, 72, 75, 78, 82, 85, 88, 92, 95, 99, 103, 106, 110, 114, 118, 122, 126, 130, 134, 139

Offset

0,12

Comments

For a guide to related sequences, see A211422.

Links

Table of n, a(n) for n=0..68.

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^8/((1-x)*(1-x^3)*(1-x^5)).

a(n) = n^2/30 - 7/30*n + O(1). - Charles R Greathouse IV, May 31 2026

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}]  (* A211524 *)
FindLinearRecurrence[t]
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1}, 69] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) a(n)=(n^2-7*n+14771042108095860\12^(n%15)%12*2)/30 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A008672, A211422.

Sequence in context: A369870 A097950 A011885 * A008672 A097923 A027582

Adjacent sequences: A211521 A211522 A211523 * A211525 A211526 A211527

Keyword

nonn,easy,changed

Author

Clark Kimberling, Apr 14 2012

Status

approved