|
| |
|
|
A095913
|
|
Number of plasma partitions of 2n-1.
|
|
1
| |
|
|
0, 0, 1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 29, 36, 44, 56, 68, 82, 101, 122, 146, 176, 210, 248, 296, 350, 410, 484, 566, 660, 772, 896, 1038, 1204, 1391, 1602, 1846, 2120, 2428, 2784, 3182, 3628, 4138, 4708, 5347, 6072, 6880, 7784, 8804, 9940, 11208, 12630
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
FORMULA
| G.f.: sum(i=1, oo, x^(i+2)/prod(j=1, i, 1-x^(2*j-1))) . - Michael Somos Aug 18 2006
|
|
|
EXAMPLE
| A plasma partition is a partition of n into 1 distinct odd part and an even number of odd parts and at least 2 parts of 1, so looking like plasma.
E.g. a(7) counts the plasma partitions of 13, has 11+1+1 = 9+1+1 = 7+1+1+1+1 = 5+1+1+1+1+1+1 = 5+3+3+1+1 = 3+1+1+1+1+1+1+1+1, so a(7)=6.
Graphically, these are;
.....*..........*........*......*.....*....*
***********.....*........*......*....***...*
.....*......*********....*......*...*****..*
................*.....*******...*....***...*
................*........*....*****...*....*
.........................*......*.........***
.........................*......*..........*
................................*..........*
................................*..........*
...........................................*
...........................................*
|
|
|
PROG
| (PARI) {a(n)=local(A); if(n<3, 0, n-=2; A=1+x*O(x^n); polcoeff( sum(k=0, n-1, A*=(x/(1-x^(2*k+1)) +x*O(x^(n-k)))), n))} /* Michael Somos Aug 18 2006 */
|
|
|
CROSSREFS
| a(n)=A053253(n-3).
Sequence in context: A014977 A008583 A053253 * A102848 A134157 A045476
Adjacent sequences: A095910 A095911 A095912 * A095914 A095915 A095916
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jul 13 2004
|
| |
|
|
