0,3

Number of 2 X n binary arrays with a path of adjacent 1's from top row to bottom row. - Ron Hardin (rhhardin(AT)att.net), Mar 21 2002

a(n)/4^n is the probability that two randomly selected (with replacement) subsets of [n] will have at least one element in common if the probability of selection is equal for all subsets. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 09 2009]

A167762,A167784. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 13 2009]

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

Index entries for sequences related to linear recurrences with constant coefficients

X. Acloque, Polynexus Numbers and other mathematical wonders.

a(n) = 4*a(n-1) + 3^(n-1) - Xavier Acloque Oct 20 2003

Binomial transform of A001047. - Ross La Haye (rlahaye(AT)new.rr.com), Sep 17 2005

G.f.: 1/(1-4*x)-1/(1-3*x). E.g.f.: e^(4*x)-e^(3*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]

a(n)=2^n*Sum_i=0...n Binomial[n,i]*(2^i-1)/2^i [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 09 2009]

a(n)=4a(n-1)+9a(n-2)-36(n-3). [From Paul Curtz (bpcrtz(AT)free.fr), Nov 13 2009]

a:=n->sum(3^(n-j)*binomial(n, j), j=1..n): seq(a(n), n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

a[n_]:=4^n-3^n; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 21 2008]

(Other) sage: [lucas_number1(n, 7, 12) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]

Sequence in context: A085720 A049494 A049495 this_sequence A099454 A125317 A006419

Adjacent sequences: A005058 A005059 A005060 this_sequence A005062 A005063 A005064

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com).