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A211440
Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and 2w+3x+3y=0.
2
1, 3, 5, 17, 23, 29, 53, 63, 73, 109, 123, 137, 185, 203, 221, 281, 303, 325, 397, 423, 449, 533, 563, 593, 689, 723, 757, 865, 903, 941, 1061, 1103, 1145, 1277, 1323, 1369, 1513, 1563, 1613, 1769, 1823, 1877, 2045, 2103, 2161, 2341, 2403, 2465
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
FORMULA
Conjectures from Colin Barker, May 15 2017: (Start)
G.f.: (1 + 3*x + x^2)*(1 - x + 4*x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)^2).
a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n>6.
(End)
From Robert Israel, Apr 03 2019: (Start)
a(3*j) = 10*j^2+6*j+1.
a(3*j+1) = 10*j^2 + 10*j + 3.
a(3*j+2) = 10*j^2 + 14*j + 5.
This has the conjectured g.f. and recurrence. (End)
MAPLE
seq(op([10*j^2+6*j+1, 10*j^2 + 10*j + 3, 10*j^2 + 14*j + 5]), j=0..30); # Robert Israel, Apr 03 2019
MATHEMATICA
t[n_] := t[n] = Flatten[Table[2 w + 3 x + 3 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 30}] (* A211440 *)
(t - 1)/2 (* integers *)
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 3, 5, 17, 23, 29, 53}, 60] (* Harvey P. Dale, Aug 29 2021 *)
CROSSREFS
Cf. A211422.
Sequence in context: A153417 A069687 A079017 * A100564 A231232 A154608
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 11 2012
STATUS
approved