particiones de un número entero

n = 1+...(n)...+1


m+(1+...(q+1)...+1) = m+(q+1)


P_{1}(n) = (n+(-1))


m+(2+...(q+1)...+2) = m+(q+1)·2


Si n=2k ==> P_{2}(n) = k+(-1) = ( (n+(-2))/2 )
Si n=2k+1 ==> P_{2}(n) = k = ( (n+(-1))/2 )


m+(3+...(q+1)...+3) = m+(q+1)·3


Si n=3k ==> P_{3}(n) = k+(-1) = ( (n+(-3))/3 )
Si n=3k+1 ==> P_{3}(n) = k = ( (n+(-1))/3 )
Si n=3k+2 ==> P_{3}(n) = k = ( (n+(-2))/3 )


m+(4+...(q+1)...+4) = m+(q+1)·4


Si n=4k ==> P_{4}(n) = k+(-1) = ( (n+(-4))/4 )
Si n=4k+1 ==> P_{4}(n) = k = ( (n+(-1))/4 )
Si n=4k+2 ==> P_{4}(n) = k = ( (n+(-2))/4 )
Si n=4k+3 ==> P_{4}(n) = k = ( (n+(-3))/4 )


m+(5+...(q+1)...+5) = m+(q+1)·5


Si n=5k ==> P_{5}(n) = k+(-2) = ( (n+(-5))/5 )
Si n=5k+1 ==> P_{5}(n) = k+(-2) = ( (n+(-1))/5 )
Si n=5k+2 ==> P_{5}(n) = k+(-1) = ( (n+(-2))/5 )
Si n=5k+3 ==> P_{5}(n) = k+(-1) = ( (n+(-3))/5 )
Si n=5k+4 ==> P_{5}(n) = k+(-1) = ( (n+(-4))/5 )




(2+...(p+2)...+2)+(1+...(q+2)...+1) = (p+2)·2+(q+2)


Si n=2k ==> P_{1,2}(n) = k+(-2) = ( (n+(-4))/2 )
Si n=2k+1 ==> P_{1,2}(n) = k+(-2) = ( (n+(-5))/2 )


(3+...(p+2)...+3)+(1+...(q+2)...+1) = (p+2)·3+(q+2)


Si n=3k ==> P_{1,3}(n) = k+(-2) = ( (n+(-6))/3 )
Si n=3k+1 ==> P_{1,3}(n) = k+(-2) = ( (n+(-7))/3 )
Si n=3k+2 ==> P_{1,3}(n) = k+(-1) = ( (n+(-5))/3 )


(4+...(p+2)...+4)+(1+...(q+2)...+1) = (p+2)·4+(q+2)


Si n=4k ==> P_{1,4}(n) = k+(-2) = ( (n+(-8))/4 )
Si n=4k+1 ==> P_{1,4}(n) = k+(-2) = ( (n+(-9))/4 )
Si n=4k+2 ==> P_{1,4}(n) = k+(-1) = ( (n+(-6))/4 )
Si n=4k+3 ==> P_{1,4}(n) = k+(-1) = ( (n+(-7))/4 )


(5+...(p+2)...+5)+(1+...(q+2)...+1) = (p+2)·5+(q+2)


Si n=5k ==> P_{1,5}(n) = k+(-2) = ( (n+(-10))/5 )
Si n=5k+1 ==> P_{1,5}(n) = k+(-2) = ( (n+(-11))/5 )
Si n=5k+2 ==> P_{1,5}(n) = k+(-1) = ( (n+(-7))/5 )
Si n=5k+3 ==> P_{1,5}(n) = k+(-1) = ( (n+(-8))/5 )
Si n=5k+4 ==> P_{1,5}(n) = k+(-1) = ( (n+(-9))/5 )






2 = 1+1


3 = 1+1+1
3 = 2+1


4 = 1+1+1+1
4 = 3+1
4 = 2+(1+1)
4 = 2+2


5 = 1+1+1+1+1
5 = 4+1
5 = 3+(1+1)
5 = 2+(1+1+1)
5 = 3+2
5 = 1+(2+2)


6 = 1+1+1+1+1+1
6 = 5+1
6 = 4+(1+1)
6 = 3+(1+1+1)
6 = 2+(1+1+1+1)
6 = 4+2
6 = 2+(2+2)
6 = 3+3
6 = (1+1)+(2+2)


7 = 1+1+1+1+1+1+1
7 = 6+1
7 = 5+(1+1)
7 = 4+(1+1+1)
7 = 3+(1+1+1+1)
7 = 2+(1+1+1+1+1)
7 = 5+2
7 = 3+(2+2)
7 = 1+(2+2+2)
7 = 4+3
7 = 1+(3+3)
7 = (1+1+1)+(2+2)


8 = 1+1+1+1+1+1+1+1
8 = 7+1
8 = 6+(1+1)
8 = 5+(1+1+1)
8 = 4+(1+1+1+1)
8 = 3+(1+1+1+1+1)
8 = 2+(1+1+1+1+1+1)
8 = 6+2
8 = 4+(2+2)
8 = 2+(2+2+2)
8 = 5+3
8 = 2+(3+3)
8 = 4+4
8 = (1+1+1+1)+(2+2)
8 = (1+1)+(2+2+2)
8 = (1+1)+(3+3)


9= 1+1+1+1+1+1+1+1+1
9 = 8+1
9 = 7+(1+1)
9 = 6+(1+1+1)
9 = 5+(1+1+1+1)
9 = 4+(1+1+1+1+1)
9 = 3+(1+1+1+1+1+1)
9 = 2+(1+1+1+1+1+1+1)
9 = 7+2
9 = 5+(2+2)
9 = 3+(2+2+2)
9 = 1+(2+2+2+2)
9 = 6+3
9 = 3+(3+3)
9 = 5+4
9 = 1+(4+4)
9 = (1+1+1+1+1)+(2+2)
9 = (1+1+1)+(2+2+2)
9 = (1+1+1)+(3+3)


10 = 1+1+1+1+1+1+1+1+1+1
10 = 9+1
10 = 8+(1+1)
10 = 7+(1+1+1)
10 = 6+(1+1+1+1)
10 = 5+(1+1+1+1+1)
10 = 4+(1+1+1+1+1+1)
10 = 3+(1+1+1+1+1+1+1)
10 = 2+(1+1+1+1+1+1+1+1)
10 = 8+2
10 = 6+(2+2)
10 = 4+(2+2+2)
10 = 2+(2+2+2+2)
10 = 7+3
10 = 4+(3+3)
10 = 1+(3+3+3)
10 = 6+4
10 = 2+(4+4)
10 = 5+5
10 = (1+1+1+1+1+1)+(2+2)
10 = (1+1+1+1)+(2+2+2)
10 = (1+1)+(2+2+2+2)
10 = (1+1+1+1)+(3+3)
10 = (1+1)+(4+4)