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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

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Last modified May 8 09:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)