##########################################################################
#  Copyright (C) 2006 Jaap Spies, jaapspies@gmail.com
#  Copyright (C) 2006 William Stein, wstein@gmail.com
#
#  Distributed under the terms of the GNU General Public License (GPL):
#
#                  http://www.gnu.org/licenses/
##########################################################################

def A079911(n):
    r"""
    function returns solutions to the Dancing School problem with 6 girls

    The value is $per(B)$, the permanent of the (0,1)-matrix $B$
    of size $6 \times 6+n$ with $b(i,j)=1$ if and only if $i \le j \le i+n$.

    We use precalculated values for $n = 0, 1, 2, 3$ For $n > 3$ we use the
    polynomial $n^6 - 9*n^5 + 60*n^4 - 225*n^3 + 555*n^2 - 774*n + 484$
    calculated with the function dance.
    See http://www.jaapspies.nl/mathfiles/dancing.sage

    See Nieuw Archief voor Wiskunde 5/7 nr. 4 December 2006 p. 285

    INPUT:
        n -- non negative number

    OUTPUT
        integer

    EXAMPLES:
        sage: A079911(2)
        79

        sage: A079911(20)
        43207004

        sage: A079911(10)
        523244

        sage: A079911(1000)
        991059775554226484


    AUTHOR:
        - Jaap Spies (2006-12-10)
    """
    b = [1, 7, 79, 478]
  
    if n >= 0 and n <= 3:
        return b[n]
    else:
        return n^6 - 9*n^5 + 60*n^4 - 225*n^3 + 555*n^2 - 774*n + 484 # dance(6)


def A079911_list(n):
    r"""
    function returns list of solutions to the Dancing School problem with 6 girls

    We use precalculated values for $n = 0, 1, 2, 3$. For $n > 3$ we use the
    polynomial $h^6 - 9*h^5 + 60*h^4 - 225*h^3 + 555*h^2 - 774*h + 484$
    calculated with the function dance.
    See http://www.jaapspies.nl/mathfiles/dancing.sage

    INPUT:
        n -- non negative number

    OUTPUT
        list of integers

    EXAMPLES:
        sage: print A079911_list(10)
        [1, 7, 79, 478, 2108, 7364, 21652, 55532, 127604, 268108, 523244]
       
        sage: print A079911_list(1)
        [1, 7]

        sage: print A079911_list(0)
        [1]


    AUTHOR:
        - Jaap Spies (2006-12-10)
    """

    h = QQ['h'].gen()

    b = [1, 7, 79, 478]
  
    if n >= 0 and n <= 3:
        return b[:n+1]
    else:
        pol =  h^6 - 9*h^5 + 60*h^4 - 225*h^3 + 555*h^2 - 774*h + 484 # dance(6)
        a = [pol(i) for i in range(4, n+1)]
        for i in range(4):
            a.insert(i,b[i])
        return a