0,2

Central coefficient of (1+2x+4x^2)^n.

Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the H steps can have 2 colors and the U steps can have 4 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 31 2008

a(n) = number of 2 by n matrices with entries in {1,2,3}, same number of 1s in top and bottom rows, and no constant columns. For example, a(1)=2 counts the transposes of (2,3) and (3,2). The number of such matrices with k 1s in each row is binom(n,2k) [choose columns containing 1s] x binom(2k,k) [place 1s in these columns] x 2^n [place 2 or 3 in the topmost available spot in each column and the other of 2,3 in the other spot if not occupied by a 1]. [From David Callan (callan(AT)stat.wisc.edu), Aug 25 2009]

Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

G.f.: 1/sqrt((1+2x)(1-6x)); E.g.f.: exp(2x)BesselI(0, 4x); a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(2(n-k), n)3^k}.

Cf. A084609, A084770.

Sequence in context: A084128 A044047 A105487 this_sequence A067125 A005038 A094780

Adjacent sequences: A098450 A098451 A098452 this_sequence A098454 A098455 A098456

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Sep 08 2004