public static void pentagon_num_test( )
//****************************************************************************80
//
// Purpose:
//
// PENTAGON_NUM_TEST tests PENTAGON_NUM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 June 2007
//
// Author:
//
// John Burkardt
//
{
int n;
Console.WriteLine("");
Console.WriteLine("PENTAGON_NUM_TEST");
Console.WriteLine(" PENTAGON_NUM computes the pentagonal numbers.");
Console.WriteLine("");
for (n = 1; n <= 10; n++)
{
Console.WriteLine(" " + n.ToString().PadLeft(4)
+ " " + Pentagon.pentagon_num(n).ToString().PadLeft(6) + "");
}
}
public static void pent_enum_test( )
//****************************************************************************80
//
// Purpose:
//
// PENT_ENUM_TEST tests PENT_ENUM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 07 March 2007
//
// Author:
//
// John Burkardt
//
{
const int N = 10;
int i;
Console.WriteLine("");
Console.WriteLine("PENT_ENUM_TEST");
Console.WriteLine(" PENT_ENUM counts points in pentagons.");
Console.WriteLine("");
Console.WriteLine(" N Pent(N)");
Console.WriteLine("");
for (i = 0; i <= N; i++)
{
Console.WriteLine(i.ToString().PadLeft(4) + " "
+ Pentagon.pentagon_num(i).ToString().PadLeft(6) + "");
}
}
public static void i4_partition_count(int n, ref int[] p)
//****************************************************************************80
//
// Purpose:
//
// I4_PARTITION_COUNT computes the number of partitions of an integer.
//
// Discussion:
//
// Partition numbers are difficult to compute. This routine uses
// Euler's method, which observes that:
//
// P(0) = 1
// P(N) = P(N-1) + P(N-2)
// - P(N-5) - P(N-7)
// + P(N-12) + P(N-15)
// - ...
//
// where the numbers 1, 2, 5, 7, ... to be subtracted from N in the
// indices are the successive pentagonal numbers, (with both positive
// and negative indices) with the summation stopping when a negative
// index is reached.
//
// First values:
//
// N P
//
// 0 1
// 1 1
// 2 2
// 3 3
// 4 5
// 5 7
// 6 11
// 7 15
// 8 22
// 9 30
// 10 42
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 28 May 2003
//
// Author:
//
// John Burkardt
//
// Reference:
//
// John Conway, Richard Guy,
// The Book of Numbers,
// Springer Verlag, 1996, page 95.
//
// Parameters:
//
// Input, int N, the index of the highest partition number desired.
//
// Output, int P[N+1], the partition numbers.
//
{
int i;
p[0] = 1;
for (i = 1; i <= n; i++)
{
p[i] = 0;
int j = 0;
int sgn = 1;
int pj;
for (;;)
{
j += 1;
pj = Pentagon.pentagon_num(j);
if (i < pj)
{
break;
}
p[i] += sgn * p[i - pj];
sgn = -sgn;
}
j = 0;
sgn = 1;
for (;;)
{
j -= 1;
pj = Pentagon.pentagon_num(j);
if (i < pj)
{
break;
}
p[i] += sgn * p[i - pj];
sgn = -sgn;
}
}
}