A095913 Number of plasma partitions of 2n-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

Offset

1,4

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Formula

G.f.: sum(i>=1, x^(i+2)/prod(j=1..i, 1-x^(2*j-1))) . - Michael Somos, Aug 18 2006

G.f.: x^2*(1 - G(0) )/(1-x) where G(k) = 1 - 1/(1-x^(2*k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 18 2013

a(n) ~ exp(Pi*sqrt(n/3)) / (4*sqrt(n)). - Vaclav Kotesovec, Jun 10 2019

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;
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.....*......*********....*......*...*****..*
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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 A260183 A134157

Adjacent sequences: A095910 A095911 A095912 * A095914 A095915 A095916

Keyword

nonn

Author

Jon Perry, Jul 13 2004

Status

approved