A211543 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x+5y.

0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 16, 18, 21, 23, 25, 28, 31, 34, 37, 40, 43, 47, 51, 54, 58, 62, 66, 71, 75, 79, 84, 89, 94, 99, 104, 109, 115, 121, 126, 132, 138, 144, 151, 157, 163, 170, 177, 184, 191, 198, 205, 213, 221, 228, 236, 244

Offset

0,8

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

Mathematica

t[n_] := t[n] = Flatten[Table[-2 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}]   (* A211543 *)
FindLinearRecurrence[t]
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {0, 0, 0, 0, 1, 1, 1, 2, 3}, 63] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(vector(4), Vec(x^4*(1 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 03 2017

Crossrefs

Cf. A211422.

Sequence in context: A327261 A337133 A062490 * A180711 A363938 A032957

Adjacent sequences: A211540 A211541 A211542 * A211544 A211545 A211546

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2012

Status

approved