login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218703 Number of partitions of n in which any two distinct parts differ by at least 8. 2
1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 4, 10, 7, 12, 13, 17, 16, 23, 21, 30, 30, 34, 35, 47, 43, 51, 52, 66, 63, 81, 77, 100, 99, 120, 121, 156, 150, 185, 189, 234, 230, 283, 281, 343, 350, 409, 414, 503, 497, 587, 600, 695, 703, 824, 830, 967, 988, 1122, 1148, 1333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also number of partitions of n in which each part, with the possible exception of the largest, occurs at least 8 times.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1 + Sum_{j>=1} x^j/(1-x^j) * Product_{i=1..j-1} (1+x^(8*i)/(1-x^i)).

EXAMPLE

a(9) = 3: [1,1,1,1,1,1,1,1,1], [3,3,3], [9].

a(10) = 5: [1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2], [5,5], [1,9], [10].

a(11) = 4: [1,1,1,1,1,1,1,1,1,1,1], [1,1,9], [1,10], [11].

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

       b(n, i-1) +add (b(n-i*j, i-8), j=1..n/i)))

    end:

a:= n-> b(n, n):

seq (a(n), n=0..70);

CROSSREFS

Column k=8 of A218698.

Sequence in context: A328871 A169819 A134681 * A326641 A144372 A182861

Adjacent sequences:  A218700 A218701 A218702 * A218704 A218705 A218706

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 04 2012

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 5 09:47 EST 2020. Contains 338945 sequences. (Running on oeis4.)