0,2

Number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = s(2n) = 2.

Number of Dyck paths of semilength n+2 with no initial and no final UD's. Example: a(2)=6 because the only Dyck paths of semilength 4 with no initial and no final UD's are: UUDUDUDD, UUDUUDDD, UUUDDUDD, UUUDUDDD, UUDDUUDD, UUUUDDDD. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 26 2003

Number of branches of length 1 starting from the root in all ordered trees with n+1 edges. Example: a(1)=2 because the tree /\ has two branches of length 1 starting from the root and the path-tree of length 2 has none. a(n)=Sum(k*A127158(n+1,k),k=0..n+1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see pp. 188, 196).

Expansion of (1+x^1*C^3)*C^1, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

a(n)=3(3n^2+3n+2)binom(2n, n)/(n+1)(n+2)(n+3) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 26 2003

a(n)=Sum_{k, 0<=k<=2}A039599(n,k)=A000108(n)+A000245(n)+A000344(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 12 2008]

T(2n, n), where T is the array defined in A026009.

Cf. A127158.

Sequence in context: A094831 A033193 A071738 this_sequence A120900 A059712 A059713

Adjacent sequences: A026009 A026010 A026011 this_sequence A026013 A026014 A026015

nonn

N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)