def test_tribonacci():
assert [tribonacci(n) for n in range(8)] == [0, 1, 1, 2, 4, 7, 13, 24]
assert tribonacci(100) == 98079530178586034536500564
assert tribonacci(0, x) == 0
assert tribonacci(1, x) == 1
assert tribonacci(2, x) == x**2
assert tribonacci(3, x) == x**4 + x
assert tribonacci(4, x) == x**6 + 2 * x**3 + 1
assert tribonacci(5, x) == x**8 + 3 * x**5 + 3 * x**2
n = Dummy('n')
assert tribonacci(n).limit(n, S.Infinity) is S.Infinity
w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2
a = (1 + cbrt(19 + 3 * sqrt(33)) + cbrt(19 - 3 * sqrt(33))) / 3
b = (1 + w * cbrt(19 + 3 * sqrt(33)) + w**2 * cbrt(19 - 3 * sqrt(33))) / 3
c = (1 + w**2 * cbrt(19 + 3 * sqrt(33)) + w * cbrt(19 - 3 * sqrt(33))) / 3
assert tribonacci(n).rewrite(sqrt) == \
(a**(n + 1)/((a - b)*(a - c))
+ b**(n + 1)/((b - a)*(b - c))
+ c**(n + 1)/((c - a)*(c - b)))
assert tribonacci(n).rewrite(sqrt).subs(n, 4).simplify() == tribonacci(4)
assert tribonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \
tribonacci(10)
assert tribonacci(n).rewrite(TribonacciConstant) == floor(
3 * TribonacciConstant**n * (102 * sqrt(33) + 586)**Rational(1, 3) /
(-2 * (102 * sqrt(33) + 586)**Rational(1, 3) + 4 +
(102 * sqrt(33) + 586)**Rational(2, 3)) + S.Half)
raises(ValueError, lambda: tribonacci(-1, x))
def test_tribonacci():
assert [tribonacci(n) for n in range(8)] == [0, 1, 1, 2, 4, 7, 13, 24]
assert tribonacci(100) == 98079530178586034536500564
assert tribonacci(0, x) == 0
assert tribonacci(1, x) == 1
assert tribonacci(2, x) == x**2
assert tribonacci(3, x) == x**4 + x
assert tribonacci(4, x) == x**6 + 2 * x**3 + 1
assert tribonacci(5, x) == x**8 + 3 * x**5 + 3 * x**2
n = Dummy('n')
assert tribonacci(n).limit(n, S.Infinity) == S.Infinity
w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2
a = (1 + cbrt(19 + 3 * sqrt(33)) + cbrt(19 - 3 * sqrt(33))) / 3
b = (1 + w * cbrt(19 + 3 * sqrt(33)) + w**2 * cbrt(19 - 3 * sqrt(33))) / 3
c = (1 + w**2 * cbrt(19 + 3 * sqrt(33)) + w * cbrt(19 - 3 * sqrt(33))) / 3
assert tribonacci(n).rewrite(sqrt) == \
(a**(n + 1)/((a - b)*(a - c))
+ b**(n + 1)/((b - a)*(b - c))
+ c**(n + 1)/((c - a)*(c - b)))
assert tribonacci(n).rewrite(sqrt).subs(n, 4).simplify() == tribonacci(4)
assert tribonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \
tribonacci(10)
def test_tribonacci():
assert [tribonacci(n) for n in range(8)] == [0, 1, 1, 2, 4, 7, 13, 24]
assert tribonacci(100) == 98079530178586034536500564
assert tribonacci(0, x) == 0
assert tribonacci(1, x) == 1
assert tribonacci(2, x) == x**2
assert tribonacci(3, x) == x**4 + x
assert tribonacci(4, x) == x**6 + 2*x**3 + 1
assert tribonacci(5, x) == x**8 + 3*x**5 + 3*x**2
n = Dummy('n')
assert tribonacci(n).limit(n, S.Infinity) == S.Infinity
w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2
a = (1 + cbrt(19 + 3*sqrt(33)) + cbrt(19 - 3*sqrt(33))) / 3
b = (1 + w*cbrt(19 + 3*sqrt(33)) + w**2*cbrt(19 - 3*sqrt(33))) / 3
c = (1 + w**2*cbrt(19 + 3*sqrt(33)) + w*cbrt(19 - 3*sqrt(33))) / 3
assert tribonacci(n).rewrite(sqrt) == \
(a**(n + 1)/((a - b)*(a - c))
+ b**(n + 1)/((b - a)*(b - c))
+ c**(n + 1)/((c - a)*(c - b)))
assert tribonacci(n).rewrite(sqrt).subs(n, 4).simplify() == tribonacci(4)
assert tribonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \
tribonacci(10)