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 A263987 Number of ways of ordering integers 1 to n such that each number is either a factor of or larger than its predecessor. 0
 1, 2, 4, 14, 28, 164, 328, 2240, 9970, 63410, 126820, 1810514, 3621028, 31417838, 294911038, 3344414606, 6688829212, 121919523980, 243839047960, 5307482547686, 56885719183654 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE For n=4, the allowable sequences are: (1,2,3,4), (1,3,4,2), (1,4,2,3), (2,1,3,4), (2,3,1,4), (2,3,4,1), (2,4,1,3), (3,1,2,4), (3,1,4,2), (3,4,1,2), (3,4,2,1), (4,1,2,3), (4,2,1,3), (4,2,3,1). MAPLE b:= proc(i, s) option remember; `if`(s={}, 1, add(       `if`(j>i or irem(i, j)=0, b(j, s minus {j}), 0), j=s))     end: a:= n-> add(b(i, {\$1..n} minus {i}), i=1..n): seq(a(n), n=1..12);  # Alois P. Heinz, Oct 31 2015 MATHEMATICA b[i_, s_] := b[i, s] = If[s == {}, 1, Sum[If[j > i || Mod[i, j] == 0, b[j, s ~Complement~ {j}], 0], {j, s}]]; a[n_] := Sum[b[i, Range[n] ~Complement~ {i}], {i, 1, n}]; Array[a, 12] (* Jean-François Alcover, Nov 28 2020, after Alois P. Heinz *) PROG (Python)# def p(n): ....count = 0 ....for i in permutations(range(1, n+1), r=n): ........for j in range(len(i)-1): ............if i[j]%i[j+1]!=0 and i[j]>i[j+1]: ................break ........else: ............count+=1 ....return count for i in range(1, 100): ....print(p(i)) (PARI) a(n) = {nb = 0; for (k=0, n!-1, perm = numtoperm(n, k); ok = 1; for (j=2, n, if ((perm[j] % perm[j-1]) && (perm[j] > perm[j-1]), ok=0; break); ); if (ok, nb++); ); nb; } \\ Michel Marcus, Nov 02 2015 CROSSREFS Sequence in context: A323656 A338740 A304341 * A333710 A295909 A095977 Adjacent sequences:  A263984 A263985 A263986 * A263988 A263989 A263990 KEYWORD nonn,more AUTHOR Matthew Scroggs, Oct 31 2015 EXTENSIONS a(11)-a(21) from Alois P. Heinz, Oct 31 2015 STATUS approved

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Last modified January 22 17:21 EST 2021. Contains 340363 sequences. (Running on oeis4.)