def getNthPellNumber(n):
'''
From: http://oeis.org/A000129:
a( n ) = round( ( 1 + sqrt( 2 ) ) ^ n )
'''
precision = int(fmul(n, 0.4))
if mp.dps < precision:
mp.dps = precision
return getNthLinearRecurrence([1, 2], [0, 1], fsub(n, 1))
def getNthNonagonalHexagonalNumberOperator(n):
# a = fmul( 3, sqrt( 7 ) )
# b = fadd( 8, a )
# c = fsub( 8, a )
# sign = 1 #power( -1, n )
# exponent = fsub( fmul( 4, n ), 4 )
# print( str( fmul( c, sign ) ) + ' ' + str( power( b, exponent ) ) )
# return floor( fprod( [ fdiv( 9, 112 ), fmul( c, sign ), power( b, exponent ) ] ) )
return getNthLinearRecurrence(
[1, -1, -4162056194, 4162056194, 1],
[1, 325, 5330229625, 1353857339341, 22184715227362706161], fsub(n, 1))
def getNthPellNumber( n ):
'''
From: http://oeis.org/A000129
a( n ) = round( ( 1 + sqrt( 2 ) ) ^ n )
'''
if n < 0:
raise ValueError( '\'nth_pell\' expects a non-negative argument' )
precision = int( fmul( n, 0.4 ) )
if ( mp.dps < precision ):
mp.dps = precision
return getNthLinearRecurrence( [ 1, 2 ], [ 0, 1 ], fsub( n, 1 ) )
def getNthNonagonalTriangularNumberOperator(n):
n = fsub(n, 1)
return getNthLinearRecurrence([1, -255, 255], [1, 325, 82621], n)
def getNthHeptagonalSquareNumberOperator(n):
index = getNthLinearRecurrence([1, -1, 0, -1442, 1442, 0, 1],
[1, 6, 49, 961, 8214, 70225, 1385329],
fsub(n, 1))
return getNthPolygonalNumber(index, 7)
def getNthHeptagonalTriangularNumberOperator(n):
return getNthLinearRecurrence([1, -1, -103682, 103682, 1],
[1, 55, 121771, 5720653, 12625478965],
fsub(n, 1))
def getNthPentagonalSquareNumberOperator(n):
return getNthLinearRecurrence([1, -9603, 9603], [1, 9801, 94109401],
fsub(n, 1))
def getNthPentagonalTriangularNumberOperator(n):
if n == 0:
return 0
return getNthLinearRecurrence([1, -195, 195], [1, 210, 40755], fsub(n, 1))