0,2

Pairwise sums of A006356. Cf. A033303, A077850. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 06 2003

Number of (3412, P)-avoiding involutions in S_{n+1}, where P={1342, 1423, 2314, 3142, 2431, 4132, 3241, 4213, 21543, 32154, 43215, 15432, 53241, 52431, 42315, 15342, 54321}. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 06 2003

Number of 31- and 22-avoiding words of length n on alphabet {1,2,3} which do not end in 3, (e.g. n=3, we have 111,112,121,132,211,212,232,321 and 332). See A028859, A001519. - Jon Perry (perry(AT)globalnet.co.uk), Aug 04 2003

Form the graph with matrix A=[1, 1, 1; 1, 0, 0; 1, 0, 1]. Then the sequence 1,1,2,4,... with g.f. (1-x-x^2)/(1-2x-x^2+x^3) counts closed walks of length n at the degree 3 vertex. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004

a(n)=number of Motzkin (n+1)-sequences whose flatsteps all occur at level <=1 and whose height is <=2. For example, a(5)=45 counts all 51 Motzkin 6-paths except FUUFDD, UFUFDD, UUFDDF, UUFDFD, UUFFDD, UUUDDD (the first five violate the flatstep restriction and the last violates the height restriction). - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004

E. S. Egge, Restricted 3412-Avoiding Involutions: Continued Fractions, Chebyshev Polynomials and Enumerations, sec. 8

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 464

G.f.: -(-1+x^2)/(x^3-x^2-2*x+1)

Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(n)-a(n+1)-2*a(n+2)+a(n+3)}

Sum(1/7*(2+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))

a(n) = central term in the (n+1)-th power of the 3 X 3 matrix (shown in the example of A066170): [1 1 1 / 1 1 0 / 1 0 0]. E.g. a(6) = 101 since the central term in M^7 = 101. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 01 2004

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

Cf. A066170.

Sequence in context: A108469 A085584 A080019 this_sequence A080135 A111099 A000632

Adjacent sequences: A052531 A052532 A052533 this_sequence A052535 A052536 A052537

easy,nonn

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000