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A036882
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Number of partitions of 5n such that cn(1,5) = cn(4,5) <= cn(2,5) = cn(3,5) <= cn(0,5).
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5
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1, 3, 8, 22, 54, 128, 282, 602, 1235, 2474, 4831, 9263, 17418, 32242, 58737, 105519, 186976, 327238, 565896, 967910, 1638175, 2745588, 4558864, 7503737, 12248234, 19835700, 31882617, 50881290, 80648122, 126998962, 198743334, 309163475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Alternatively, number of partitions of 5n such that cn(2,5) = cn(3,5) <= cn(1,5) = cn(4,5) <= cn(0,5).
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
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LINKS
| Index and properties of sequences related to partitions of 5n
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FORMULA
| a(n) = A036889(n) + A036887(n)
a(n) = A202085(n) + A036891(n)
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MAPLE
| Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 07 2009: (Start)
mkl:= proc(i, l) local ll, x, j; j:= irem (i, 5); j:= `if` (j=0, 5, j); ll:= applyop (x->x+1, j, l); map (x-> x-min(ll[]), ll) end:
g:= proc (n, i, t) local x; if n<0 then 0 elif n=0 then `if` (t[1]=t[4] and t[4]<=t[2] and t[2]=t[3] and t[3]<=t[5], 1, 0) elif i=0 then 0 elif i=1 then g (0, 0, applyop (x-> x+n, 1, t)) elif i=2 then `if` (t[2]>t[3], 0, g (n-2*(t[3]-t[2]), 1, subsop(2=t[3], t))) elif (i=3 or i=4) and t[i]>t[5] then 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=1..15); (End)
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CROSSREFS
| Sequence in context: A027211 A027235 A086596 * A020962 A027243 A110239
Adjacent sequences: A036879 A036880 A036881 * A036883 A036884 A036885
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| a(10)-a(32) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 07 2009
Edited by Max Alekseyev (maxale(AT)gmail.com), Dec 11 2011
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