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A218700 Number of partitions of n in which any two distinct parts differ by at least 5. 2
1, 1, 2, 2, 3, 2, 4, 3, 6, 7, 9, 10, 15, 15, 19, 23, 26, 28, 36, 37, 48, 52, 62, 67, 85, 93, 110, 122, 144, 157, 194, 205, 241, 265, 304, 338, 391, 422, 483, 533, 607, 661, 760, 822, 933, 1032, 1151, 1260, 1432, 1554, 1751, 1920, 2137, 2333, 2621, 2848, 3176 (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 5 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^(5*i)/(1-x^i)).

EXAMPLE

a(6) = 4: [1,1,1,1,1,1], [2,2,2], [3,3], [6].

a(7) = 3: [1,1,1,1,1,1,1], [1,6], [7].

a(8) = 6: [1,1,1,1,1,1,1,1], [2,2,2,2], [4,4], [1,1,6], [1,7], [8].

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-5), j=1..n/i)))

    end:

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

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

CROSSREFS

Column k=5 of A218698.

Sequence in context: A307995 A061889 A240089 * A325331 A333108 A266935

Adjacent sequences:  A218697 A218698 A218699 * A218701 A218702 A218703

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 04 2012

STATUS

approved

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Last modified June 2 15:41 EDT 2020. Contains 334787 sequences. (Running on oeis4.)