A211436 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and 2w+3x+4y=0.

1, 1, 7, 11, 21, 27, 43, 51, 73, 83, 109, 123, 155, 169, 207, 225, 267, 287, 335, 357, 411, 435, 493, 521, 585, 613, 683, 715, 789, 823, 903, 939, 1025, 1063, 1153, 1195, 1291, 1333, 1435, 1481, 1587, 1635, 1747, 1797, 1915, 1967, 2089, 2145

Offset

0,3

Comments

For a guide to related sequences, see A211422.

Links

Table of n, a(n) for n=0..47.

Formula

Empirical g.f.: (1 + x + 6*x^2 + 9*x^3 + 12*x^4 + 9*x^5 + 6*x^6 + x^7 + x^8) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 15 2017

Mathematica

t[n_] := t[n] = Flatten[Table[2 w + 3 x + 4 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 80}]  (* A211436 *)
(t - 1)/2                    (* integers *)

Crossrefs

Cf. A211422.

Sequence in context: A356710 A194828 A035704 * A259260 A081352 A190673

Adjacent sequences: A211433 A211434 A211435 * A211437 A211438 A211439

Keyword

nonn

Author

Clark Kimberling, Apr 11 2012

Status

approved