|
| |
|
|
A046787
|
|
Number of partitions of 5n with equal nonzero number of parts congruent to each of 1, 2, 3 and 4 modulo 5.
|
|
2
| |
|
|
0, 0, 1, 5, 17, 46, 113, 254, 546, 1122, 2242, 4354, 8286, 15441, 28303, 51025, 90699, 159003, 275355, 471216, 797761, 1336686, 2218393, 3648177, 5948503, 9620406, 15439833, 24597942, 38916192, 61159549, 95508014, 148241050, 228753319
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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.
|
|
|
LINKS
| Index and properties of sequences related to partitions of 5n
|
|
|
FORMULA
| a(n) = A046776(n) + A202086(n) + A202088(n) - A000041(n) = A202192(n) - A000041(n). [From Max Alekseyev]
|
|
|
MAPLE
| Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 04 2009: (Start)
mkl:= proc(i, l) local ll, mn, x; ll:= `if`(irem(i, 5)=0, l, applyop (x->x+1, irem(i, 5), l)); mn:= min (l[])-1; `if`(mn<=0, ll, map (x->x-mn, ll)) end:
g:= proc (n, i, t) local m, mx; if n<0 then 0 elif n=0 then `if` (t[1]>0 and t[1]=t[2] and t[2]=t[3] and t[3]=t[4], 1, 0) elif i=0 then 0 elif i<5 then mx:= max (t[]); m:= n-10*mx +t[1] +t[2]*2 +t[3]*3 +t[4]*4; `if`(m>=0 and irem(m, 10)=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]): seq (a(n), n=0..20); (End)
|
|
|
CROSSREFS
| Cf. A046776, A202192
Sequence in context: A147043 A146264 A146216 * A003295 A011853 A136303
Adjacent sequences: A046784 A046785 A046786 * A046788 A046789 A046790
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
EXTENSIONS
| a(17)-a(32) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 04 2009
|
| |
|
|
