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A109655
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Number of partitions of n^2 into up to n parts each no more than 2n, or of n(3n+1)/2 into exactly n distinct parts each no more than 3n.
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5
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1, 1, 3, 8, 33, 141, 676, 3370, 17575, 94257, 517971, 2900900, 16509188, 95220378, 555546058, 3273480400, 19456066175, 116521302221, 702567455381, 4261765991164, 25992285913221, 159303547578873, 980701254662294, 6061894625462492, 37609015174472628
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..100
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FORMULA
| a(n) =A067059(n, 2n) =A067059(2n, n). Slightly less than but close to (27/4)^n*sqrt(3)/(2*pi*n^2).
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EXAMPLE
| a(3)=8 since 3^2=9 can be partitioned into 3+3+3, 4+3+2, 4+4+1, 5+4, 5+3+1, 5+2+2, 6+3, or 6+2+1, while 3*(3*3+1)/2=15 can be partitioned into 6+5+4, 7+5+3, 7+6+2, 8+6+1, 8+5+2, 8+4+3, 9+5+1, or 9+4+2.
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MAPLE
| b:= proc(n, i, t) option remember;
`if` (i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
`if` (n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
end:
a:= n-> b(n*(3*n+1)/2, 3*n, n):
seq (a(n), n=0..20); # Alois P. Heinz, Jan 18 2012
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CROSSREFS
| A161407. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2009]
Row n=3 of A204459. - Alois P. Heinz, Jan 18 2012
Sequence in context: A148917 A120892 A195499 * A184255 A001120 A117722
Adjacent sequences: A109652 A109653 A109654 * A109656 A109657 A109658
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 05 2005
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jan 18 2012
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