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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184996 For each ordered partition of n with k numbers, remove 1 from each part and add the number k to get a new partition, until a partition is repeated. Among all ordered partitions of n, a(n) gives the maximum number of steps needed to reach a period. 1
0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 15, 16, 17, 22, 24, 24, 22, 23, 26, 33, 35, 35, 29, 30, 31, 38, 46, 48, 48, 41, 38, 39, 43, 52, 61, 63, 63, 55, 47, 48, 49, 58, 68, 78, 80, 80, 71, 62, 58, 59, 64, 75, 86, 97, 99, 99, 89, 79, 69, 70, 71, 82, 94, 106, 118, 120, 120, 109, 98, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If one plays with p(n,n) unordered partitions, one gets the same number and length of periods.

If one removes the first part z(1) of each  partition and adds 1 to the next z(1) parts to get a new partition, until a partition is repeated, one gets the same length and number of periods, playing with 2^(n-1) ordered or p(n,n) unordered partitions (A185700, A092964, A037306)

REFERENCES

R. Baumann, Computer-Knobelei, LOGIN, 4 (1987), pages ?.

H. R. Halder and W. Heise, Einf├╝hrung in Kombinatorik, Hanser Verlag, Munich, 1976, pp. 75ff.

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a((k^2+k-2)/2-j)=k^2-3-(k+1)*j with 0<=j<=(k-4) div 2 and 4<=k.

a((k^2+k+2)/2+j)=k^2-1-k*j with 0<=j<=(k-5) div 2 and 5<=k.

a((k^2+2*k-2+k mod 2)/2+j)=(k^2+4*k-2+k mod 2)/2+j with 0<=j<=2-k mod 2 and 4<=k.

a(T(k))=k^2-1 with 1<= k  for all triangular numbers T(k).

EXAMPLE

For k=6: a(19)=26; a(20)=3; a(21)=35; a(22)=35; a(23)=29; a(24)=30; a(25)=31.

For n=4: (1+1+1+1)->(4)->(3+1)->(2+2)->(1+1+2)->(1+3)--> a(4)=5 steps.

For n=5: (1+1+1+1+1)->(5)->(4+1)->(3+2)->(2+1+2)->(1+1+3)->(2+3)->(1+2+2)--> a(5)=7 steps.

CROSSREFS

Cf. A185700, A092964, A037306.

Sequence in context: A300737 A062958 A295075 * A153309 A047486 A229838

Adjacent sequences:  A184993 A184994 A184995 * A184997 A184998 A184999

KEYWORD

nonn

AUTHOR

Paul Weisenhorn, Mar 28 2011

EXTENSIONS

Partially edited by N. J. A. Sloane, Apr 08 2011

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 December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)