OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1)
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 11 2012
STATUS
approved