The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A095913 Number of plasma partitions of 2n-1. 2
 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; text; internal format)
 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; .....*..........*........*......*.....*....* ***********.....*........*......*....***...* .....*......*********....*......*...*****..* ................*.....*******...*....***...* ................*........*....*****...*....* .........................*......*.........*** .........................*......*..........* ................................*..........* ................................*..........* ...........................................* ...........................................* 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 10:39 EST 2022. Contains 358411 sequences. (Running on oeis4.)