A211536 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=4x-5y.

0, 0, 0, 2, 3, 4, 6, 8, 11, 14, 17, 21, 24, 29, 34, 39, 44, 49, 56, 63, 69, 76, 83, 92, 100, 108, 117, 126, 136, 146, 156, 167, 177, 189, 201, 213, 225, 237, 251, 265, 278, 292, 306, 322, 337, 352, 368, 384, 401, 418, 435, 453, 470, 489, 508, 527, 546

Offset

0,4

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).

Formula

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

G.f.: x^3*(2 + x + x^2 + 2*x^3 + x^6) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 03 2017

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}]  (* A211536 *)
FindLinearRecurrence[t]
LinearRecurrence[{1, 0, 0, 1, 0, -1, 0, 0, -1, 1}, {0, 0, 0, 2, 3, 4, 6, 8, 11, 14}, 57] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(vector(3), Vec(x^3*(2 + x + x^2 + 2*x^3 + x^6) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 03 2017

Crossrefs

Cf. A211422.

Sequence in context: A242110 A371069 A056829 * A071764 A238381 A290743

Adjacent sequences: A211533 A211534 A211535 * A211537 A211538 A211539

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2012

Status

approved