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Search: id:A095913
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| A095913 |
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Number of plasma partitions of 2n-1. |
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+0
2
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| 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; listen)
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OFFSET
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1,4
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FORMULA
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G.f.: sum(i=1, oo, x^(i+2)/prod(j=1, i, 1-x^(2*j-1))) . - Michael Somos Aug 18 2006
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EXAMPLE
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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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PROGRAM
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(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 */
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CROSSREFS
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a(n)=A053253(n-3).
Sequence in context: A014977 A008583 A053253 this_sequence A102848 A134157 A045476
Adjacent sequences: A095910 A095911 A095912 this_sequence A095914 A095915 A095916
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jul 13 2004
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