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 A327710 Number of compositions of n into distinct parts such that the difference between any two parts is at least two. 3
 1, 1, 1, 1, 3, 3, 5, 5, 7, 13, 15, 21, 29, 35, 43, 55, 87, 99, 137, 173, 235, 277, 363, 429, 545, 755, 895, 1135, 1443, 1827, 2285, 2837, 3463, 4285, 5199, 6309, 8237, 9755, 12091, 14743, 18351, 22251, 27833, 33125, 40819, 49045, 59691, 70869, 86033, 106163 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS All terms are odd. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = Sum_{k>=0} k! * A268187(n,k). EXAMPLE a(9) = 13: 135, 153, 315, 351, 513, 531, 36, 63, 27, 72, 18, 81, 9. MAPLE b:= proc(n, i, p) option remember; `if`(i*(i+1)/2 b(n\$2, 0): seq(a(n), n=0..50); # second Maple program: b:= proc(n, i) option remember; `if`(n=0, 1,      `if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i))))     end: a:= n-> add(k!*b(n-k^2, k), k=0..floor(sqrt(n))): seq(a(n), n=0..50); CROSSREFS Cf. A003114, A032020, A268187, A268188, A328222. Sequence in context: A237714 A245145 A092316 * A142456 A098508 A051593 Adjacent sequences:  A327707 A327708 A327709 * A327711 A327712 A327713 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 24 2020 STATUS approved

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Last modified August 12 12:23 EDT 2020. Contains 336439 sequences. (Running on oeis4.)