0,2

Total number of pairs (a_i,a_(i+1)) in all permutations on [n] such that a_i,a_(i+1) are consecutive integers. - David Callan (callan(AT)stat.wisc.edu), Nov 04 2003

Number of permutations of {1,2,...,n+2} such that there is exactly one entry between the entries 1 and 2. Example: a(2)=8 because we have 1324, 1423, 2314, 2413, 3142, 4132, 3241 and 4231. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008

a(n)=A138770(n+2,1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008

Number of permutations of 0 to n distinct letters (ABC...) 1 times ("-" (0), A (1), AB (1-1), ABC (1-1-1), ABCD (1-1-1-1 )etc...) and one after the other to resemble motif:( "-",... BB (0-2), ABB (1-2-0), AABB (2-2-0-0), AAABB (3-2-0-0-0) AAAABB (4-2-0-0-0-0), AAAAABB (5-2-0-0-0-0-0), AAAAAABB (6-2-0-0-0-0-0-0), etc... 0 fixed point (or free fixed point). Example: if ABC (1-1-1) and motif ABB (1-2-0) then 2 * 0 (free) fixed point, if ABCD (1-1-1-1), and motif AABB (2-2-0-0) then 8 * 0 (free) fixed point, if ABCDE (1-1-1-1-1), and motif AAABB (3-2-0-0-0), then 36 * 0 (free) fixed point, if ABCDEF (1-1-1-1-1-1), and motif AAAABB (4-2-0-0-0-0), then 192 * 0 (free) fixed point, if ABCDEFG (1-1-1-1-1-1-1), and motif AAAAABB (5-2-0-0-0-0-0), then 1200 * 0 (free) fixed point, etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2009]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 526

E.g.f.: 2*x/(-1+x)^2

Recurrence: {a(0)=0, a(1)=2, (-n^2-2*n-1)*a(n)+a(n+1)*n}

2*n*n!

spec := [S, {S=Prod(Sequence(Z), Sequence(Z), Union(Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Cf. A138770.

Sequence in context: A081958 A001540 A129044 this_sequence A020021 A052618 A055142

Adjacent sequences: A052579 A052580 A052581 this_sequence A052583 A052584 A052585

easy,nonn

encyclopedia(AT)pommard.inria.fr, Jan 25 2000