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 A285672 Number of permutations p of [n] avoiding consecutive odd sums i+p(i), (i+1)+p(i+1) for all i in [n-1]. 3
 1, 1, 1, 2, 8, 36, 180, 1008, 6336, 46080, 374400, 3369600, 32659200, 344736000, 3886444800, 47348582400, 611264102400, 8442272563200, 122595843686400, 1890952003584000, 30510694932480000, 520011800985600000, 9231875243458560000, 172292221923655680000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..466 EXAMPLE a(0) = 1: the empty permutation. a(1) = 1: 1. a(2) = 1: 12. a(3) = 2: 123, 321. a(4) = 8: 1234, 1432, 2413, 2431, 3214, 3412, 4213, 4231. a(5) = 36: 12345, 12543, 13524, 13542, 14325, 14523, 15324, 15342, 24135, 24153, 24315, 24351, 24513, 24531, 31524, 31542, 32145, 32541, 34125, 34521, 35124, 35142, 42135, 42153, 42315, 42351, 42513, 42531, 51324, 51342, 52143, 52341, 53124, 53142, 54123, 54321. MAPLE b:= proc(n, i, j, p, t) option remember; `if`(n=0, 1,      `if`(i=0 or t=1 and p=1, 0, i*b(n-1, i-1, j, 1-p, p))+      `if`(j=0 or t=1 and p=0, 0, j*b(n-1, i, j-1, 1-p, 1-p)))     end: a:= n-> b(n, floor(n/2), ceil(n/2), 1, 0): seq(a(n), n=0..25); MATHEMATICA b[n_, i_, j_, p_, t_] := b[n, i, j, p, t] =      If[n==0, 1, If[i==0 || t ==1 && p==1, 0, i*b[n-1, i-1, j, 1-p, p]] +      If[j==0 || t==1 && p==0, 0, j*b[n-1, i, j-1, 1-p, 1-p]]]; a[n_] := b[n, Floor[n/2], Ceiling[n/2], 1, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 30 2021, after Alois P. Heinz *) CROSSREFS Cf. A199660, A231601. Sequence in context: A227791 A245102 A129148 * A081958 A316663 A243948 Adjacent sequences:  A285669 A285670 A285671 * A285673 A285674 A285675 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 24 2017 STATUS approved

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Last modified January 27 16:30 EST 2022. Contains 350608 sequences. (Running on oeis4.)