def _autoFloat(f):
from math import log10 as mloggg
digits = (mloggg(f)) + 1
if (digits > 15):
return mmmfloat(f)
else:
return mmmint(f)
def getSchroderTriangle(n=5, b=True):
from sympy import Float as mmmfloat
from math import log10 as mloggg
colk = [k for k in range(n + 1)]
a = [[1 if (j == 0) else 0 for j in colk] for i in colk]
a[1][1] = 2
for i in range(1, n + 1):
for j in range(1, i + 1):
a[i][j] = a[i][j - 1] + a[i - 1][j - 1] + a[i - 1][j]
if (b):
if ((mloggg(a[i][j])) + 1 > 15):
a[i][j] = mmmfloat(a[i][j])
return a
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)