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Search: id:A046776
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| A046776 |
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Number of partitions of n with equal number of parts congruent to each of 0, 1, 2, 3 and 4 (mod 5). |
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+0
2
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| 1, 0, 0, 1, 5, 15, 36, 75, 146, 271, 495, 891, 1601, 2851, 5051, 8851, 15362, 26331, 44642, 74787, 123991, 203433, 330717, 532872, 851779, 1351147, 2128324, 3330059, 5177768, 8002170, 12296754, 18791945, 28566751, 43204575, 65022987, 97395386
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of partitions of m with equal numbers of parts congruent to each of 1, 2, 3 and 4 (mod 5) is 0 unless m == 0 mod 5.
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MAPLE
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Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 04 2009: (Start)
mkl:= proc(i, l) local ll, mn, ii, x; ii:= irem(i, 5); ii:= `if` (ii=0, 5, ii); ll:= applyop (x->x+1, ii, l); mn:= min (l[]); `if`(mn=0, ll, map (x->x-mn, ll)) end:
g:= proc (n, i, t) local m, mx, j; if n<0 then 0 elif n=0 then `if` (nops ({t[]})=1, 1, 0) elif i=0 then 0 elif i<6 then mx:= max (t[]); m:= n-15*mx +add (t[j]*j, j=1..5); g(n, i, t):= `if`(m>=0 and irem (m, 15)=0, 1, 0) else g(n, i, t):= g (n, i-1, t) + g (n-i, i, mkl(i, t)) fi end:
a:= n-> g (5*n, 5*n, [0, 0, 0, 0, 0]): seq (a(n), n=0..20); (End)
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CROSSREFS
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Cf. A046787.
Sequence in context: A093802 A006008 A086716 this_sequence A144898 A053808 A163250
Adjacent sequences: A046773 A046774 A046775 this_sequence A046777 A046778 A046779
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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a(18) - a(35) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 04 2009
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