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A218702 Number of partitions of n in which any two distinct parts differ by at least 7. 2
1, 1, 2, 2, 3, 2, 4, 2, 4, 4, 6, 6, 11, 10, 13, 16, 19, 20, 25, 27, 33, 34, 39, 41, 51, 52, 61, 65, 80, 82, 99, 104, 126, 133, 156, 168, 199, 209, 243, 261, 302, 320, 372, 392, 447, 479, 537, 572, 650, 693, 770, 829, 920, 982, 1096, 1169, 1306, 1396, 1541 (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 7 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^(7*i)/(1-x^i)).

EXAMPLE

a(8) = 4: [1,1,1,1,1,1,1,1], [2,2,2,2], [4,4], [8].

a(9) = 4: [1,1,1,1,1,1,1,1,1], [3,3,3], [1,8], [9].

a(10) = 6: [1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2], [5,5], [1,1,8], [1,9], [10].

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-7), j=1..n/i)))

    end:

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

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

CROSSREFS

Column k=7 of A218698.

Sequence in context: A049238 A001616 A257599 * A324181 A297169 A318835

Adjacent sequences:  A218699 A218700 A218701 * A218703 A218704 A218705

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 04 2012

STATUS

approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)