|
| |
|
|
A036890
|
|
Number of partitions of 5n such that cn(1,5) = cn(4,5) < cn(0,5) <= cn(2,5) = cn(3,5).
|
|
5
| |
|
|
0, 1, 4, 11, 27, 63, 142, 312, 665, 1382, 2795, 5524, 10674, 20228, 37634, 68886, 124179, 220779, 387458, 671883, 1152027, 1954614, 3283494, 5464437, 9013558, 14743397, 23923577, 38526121, 61593796, 97795238, 154251217, 241765892, 376643803, 583370176
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Alternatively, number of partitions of 5n such that cn(2,5) = cn(3,5) < cn(0,5) <= cn(1,5) = cn(4,5).
For a given partition, cn(i,n) means the number of its parts equal to i modulo n.
|
|
|
LINKS
| Index and properties of sequences related to partitions of 5n
|
|
|
FORMULA
| a(n) = A036892(n) + A036894(n)
a(n) = A036881(n) - A036884(n)
|
|
|
MAPLE
| Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 02 2009: (Start)
mkl:= proc(i, l) local ll, mn, x; ll:= applyop (x->x+1, irem (i, 5)+1, l); mn:= min (ll[]); `if` (mn=0, ll, map (x->x-mn, ll)) end:
g:= proc (n, i, t) if n<0 then 0 elif n=0 then `if` (t[2]=t[5] and t[3]=t[4] and t[5]<t[1] and t[1]<=t[3], 1, 0) elif i=0 then 0 elif i=1 then g (0, 0, [t[1], t[2]+n, t[3], t[4], t[5]]) elif i=2 then `if` (t[3]>t[4], 0, g(n-2*(t[4]-t[3]), 1, [t[1], t[2], t[4], t[4], t[5]])) 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)
|
|
|
CROSSREFS
| Sequence in context: A160399 A119706 A034345 * A000253 A047859 A100335
Adjacent sequences: A036887 A036888 A036889 * A036891 A036892 A036893
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
EXTENSIONS
| a(10)-a(32) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 02 2009
a(33)-a(34) from Max Alekseyev (maxale(AT)gmail.com), Dec 11 2011
|
| |
|
|
