A211542 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=4y-3x.

0, 0, 1, 2, 3, 5, 8, 10, 14, 17, 22, 26, 32, 36, 44, 49, 57, 63, 73, 79, 90, 97, 109, 117, 130, 138, 153, 162, 177, 187, 204, 214, 232, 243, 262, 274, 294, 306, 328, 341, 363, 377, 401, 415, 440, 455, 481, 497, 524, 540, 569, 586, 615, 633, 664, 682, 714

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

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[2 w + 3 x - 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 80}]  (* A211542 *)
FindLinearRecurrence[t]
LinearRecurrence[{0,1,1,1,-1,-1,-1,0,1},{0,0,1,2,3,5,8,10,14},57] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(vector(2), Vec(x^2*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Dec 03 2017

Formula

a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9).

G.f.: x^2*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Dec 03 2017