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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 Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz) FORMULA G.f.: 1 + Sum_{j>=1} x^j/(1-x^j) * Product_{i=1..j-1} (1+x^(8*i)/(1-x^i)). log(a(n)) ~ sqrt((2*Pi^2/3 + 4*c)*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-8*x)) dx = -1.1447921975208768146551512630331558734964408879... - Vaclav Kotesovec, Jan 28 2022 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. Cf. A160978. 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 April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)