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A046776
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Number of partitions of 5n with equal number of parts congruent to each of 0, 1, 2, 3 and 4 (mod 5).
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11
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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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LINKS
| Index and properties of sequences related to partitions of 5n
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FORMULA
| a(n) = A202085(n) - A202086(n)
a(n) = A036884(n) - A036886(n)
a(n) = A036889(n) - A036892(n)
a(n) = A202087(n) - A202088(n)
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MAPLE
| 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
| Cf. A046787.
Sequence in context: A093802 A006008 A086716 * A144898 A163250 A053808
Adjacent sequences: A046773 A046774 A046775 * A046777 A046778 A046779
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| a(18)-a(35) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 04 2009
Edited by Max Alekseyev (maxale(AT)gmail.com), Dec 11 2011
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