login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046787 Number of partitions of 5n with equal nonzero number of parts congruent to each of 1, 2, 3 and 4 modulo 5. 3
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, 351022425, 535760584 (list; graph; refs; listen; history; text; 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

Alois P. Heinz, Table of n, a(n) for n = 0..100

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). - Max Alekseyev

MAPLE

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);  # Alois P. Heinz, Jul 04 2009

MATHEMATICA

mkl[i_, l_] := Module[{ll, mn, x}, ll = If[Mod[i, 5] == 0, l, MapAt[#+1&, l, Mod[i, 5]]]; mn = Min[l]-1; If[mn <= 0, ll, Map[#-mn&, ll]]];

g[n_, i_, t_] := g[n, i, t] = Module[{m, mx}, If[n<0, 0, If[n==0, If[ t[[1]]>0 && Equal @@ t[[1;; 4]], 1, 0], If[i==0, 0, If[i<5, mx = Max[t]; m = n - 10 mx + t[[1]] + 2 t[[2]] + 3 t[[3]] + 4 t[[4]]; If[m >= 0 && Mod[m, 10]==0, 1, 0], g[n, i-1, t] + g[n-i, i, mkl[i, t]]]]]]];

a[n_] := g[5n, 5n, {0, 0, 0, 0}];

Table[a[n], {n, 0, 34}] (* Jean-Fran├žois Alcover, May 25 2019, after Alois P. Heinz *)

CROSSREFS

Cf. A046776, A202192.

Sequence in context: A147043 A146264 A146216 * A003295 A228857 A253427

Adjacent sequences:  A046784 A046785 A046786 * A046788 A046789 A046790

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

a(17)-a(32) from Alois P. Heinz, Jul 04 2009

a(33)-a(34) from Alois P. Heinz, Aug 13 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 23 22:20 EDT 2019. Contains 326254 sequences. (Running on oeis4.)