r""" Python module for OEIS sequence number A126257. Number of distinct new terms in row n of Pascal's triangle. Examples of use. ----------------------------------------------------------------------- >>> from a126257 import * >>> print a126257_list(18) [1, 0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 5, 7, 8] >>> print a126257_offset 0 >>> for x in a126257_list_pairs(6): ... print x ... (0, 1) (1, 0) (2, 1) (3, 1) (4, 2) (5, 2) >>> print a126257(7) 3 ----------------------------------------------------------------------- """ from itertools import islice, izip, count __all__ = ('a126257_offset', 'a126257_list', 'a126257_list_pairs', 'a126257', 'a126257_gen') __author__ = 'Nick Hobson <nickh@qbyte.org>' a126257_offset = offset = 0 def a126257_gen(): """Generator function for OEIS sequence A126257.""" s = set([1]) yield len(s) for row in count(1): last = len(s) x = row s.add(x) for m in xrange(1, row//2 + 1): x = (x * (row - m)) / (m + 1) s.add(x) yield len(s) - last def a126257_list(n): """Returns a list of the first n >= 0 terms.""" if n < 0: raise ValueError, 'Input must be a non-negative integer' return list(islice(a126257_gen(), n)) def a126257_list_pairs(n): """Returns a list of tuples (n, a(n)) of the first n >= 0 terms.""" if n < 0: raise ValueError, 'Input must be a non-negative integer' return list(izip(xrange(offset, n+offset), a126257_gen())) def a126257(n): """Returns the term with index n >= 0; offset 0.""" if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset) return list(islice(a126257_gen(), n-offset, n-offset+1)).pop()