def _autoFloat(f):
from math import log10 as mloggg
digits = (mloggg(f)) + 1
if (digits > 15):
return mmmfloat(f)
else:
return mmmint(f)
def CompanionPellLucasNumber(Pell, roundi=True):
from sympy import Integer as mmmint
from sympy import N as mmmn
r = Pell * (2**(1 / 2))
if (roundi):
return mmmint(r)
else:
return mmmn(r)
def Binetformula(index, roundi=True):
from sympy import Pow as mmmpow
from sympy import Integer as mmmint
from sympy import N as mmmn
b = (mmmpow(1.6185, index) - mmmpow(-0.6185, index)) / 2.237
if (not roundi):
return mmmint(b)
else:
return mmmn(b)
def LucasNumber(index, roundi=True):
from sympy import Pow as mmmpow
from sympy import Integer as mmmint
from sympy import N as mmmrat
b = (mmmpow(((1 + 5**(1 / 2)) / 2), index)) + (mmmpow(
((1 - 5**(1 / 2)) / 2), index))
if (not roundi):
return mmmint(b)
else:
return mmmrat(b)
def CompanionPellNumber(index=1, roundi=True):
from sympy import Pow as mmmpow
from sympy import Integer as mmmint
from sympy import N as mmmn
q = 2**(1 / 2)
r = (mmmpow(1 + q, index) - mmmpow(1 - q, index)) / (2)
if (roundi):
return mmmint(r)
else:
return mmmn(r)
def Binetformula(index=1, roundi=True):
from sympy import Pow as mmmpow
from sympy import Integer as mmmint
from sympy import N as mmmn
q = 2**(1 / 2)
r = (mmmpow(1 + q, index) - mmmpow(1 - q, index)) / (2 * q)
if (roundi):
return mmmint(r)
else:
return mmmn(r)
def DelannoySequence(n=5, returni=False, roundt=True):
from sympy import Integer as mmmint
from sympy import Float as mmmfloat
a = [1, 3]
for i in range(2, n + 2):
b = (3 * (2 * i - 1) * a[i - 1] - (i - 1) * a[i - 2]) / i
if (roundt == True):
b = mmmint(b)
else:
b = mmmfloat(b)
a.append(b)
if (not returni):
print(b, end=", ")
if (returni):
return a[:n]
def SchroderHipparchusSequence(n=5, returni=False, roundt=True):
from sympy import Integer as mmmint
from sympy import Float as mmmfloat
a = [1, 1, 3]
for i in range(3, n + 3):
b = ((6 * (i + 1) - 9) * a[i - 1] - (i - 2) * a[i - 2]) / (i + 1)
if (roundt == True):
b = mmmint(b)
else:
b = mmmfloat(b)
a.append(b)
if (not returni):
print(b, end=", ")
if (returni):
return a[:n]
#SchroderHipparchusSequence(10,False,False)
#SchroderHipparchusSequence(10,True)
def MotzkinSequence(n=5, returni=False, roundt=True):
from sympy import Integer as mmmint
from sympy import Float as mmmfloat
a = [1, 1, 2]
for i in range(3, n + 3):
b = ((((2 * i + 1) / (i + 2)) * a[i - 1]) + (((3 * i - 3) /
(i + 2)) * a[i - 2]))
if (roundt == True):
b = mmmint(b)
else:
b = mmmfloat(b)
a.append(b)
if (not returni):
print(b, end=", ")
if (returni):
return a[:n]
#MotzkinSequence(1000,False,False)
#MotzkinSequence(1000,False)