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Search: id:A128508
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| A128508 |
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Number of partitions p of n such that max(p)-min(p)=3. |
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1
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| 0, 0, 0, 0, 1, 1, 3, 3, 7, 7, 12, 14, 20, 22, 32, 34, 45, 51, 63, 69, 87, 93, 112, 124, 144, 156, 184, 196, 225, 245, 275, 295, 335, 355, 396, 426, 468, 498, 552, 582, 637, 679, 735, 777, 847, 889, 960, 1016, 1088, 1144, 1232, 1288, 1377, 1449, 1539, 1611, 1719
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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See A008805 and A049820 for the numbers of partitions p of n such that max(p)-min(p)=1 or 2, respectively.
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FORMULA
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Conjecture. a(1)=0 and, for n>1, a(n+1)=a(n)+d(n), where d(n) is defined as follows: d=0,0,0,1,0 for n=1,...,5 and, for n>5, d(n)=d(n-2)+1 if n=6k or n=6k+4, d(n)=d(n-2) if n=6k+1 or n=6k+3, d(n)=d(n-2)+2Floor[n/6] if n=6k+2 and d(n)=d(n-5) if n=6k+5.
G.f. for number of partitions p of n such that max(p)-min(p) = m is Sum_{k>0} x^(2*k+m)/Product_{i=0..m} (1-x^(k+i)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 04 2007
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CROSSREFS
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Cf. A008805, A049820.
Sequence in context: A088147 A109579 A109580 this_sequence A083743 A126990 A128498
Adjacent sequences: A128505 A128506 A128507 this_sequence A128509 A128510 A128511
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), May 07 2007
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 04 2007
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