0,1

Warning: there is a considerable overlap between this entry and the essentially identical A025192. A025192 is the main entry.

Number of tilings of a 4 X 4n+4 rectangle into T tetrominoes.

Numbers n such that 3^n = n/2 mod n. Cf. A066601 3^n mod n. - Zak Seidov, Aug 26 2006, Nov 20 2008

For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3} we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 27 2007

a(n)=EulerPhi[3^n] [From Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008]

a(n) = A048473+1 = A048473+A000012. a(n) = A052919(n+1)-1. a(n) = A115099-2. a(n) = A100774+2. See A007395. [From Paul Curtz (bpcrtz(AT)free.fr), Jan 20 2009]

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 203).

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..200

Index entries for sequences related to linear recurrences with constant coefficients

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 170

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Tanya Khovanova, Recursive Sequences

C. Moore, [math/9905012] Some Polyomino Tilings of the Plane

a(n) = 2*3^n; a(n) = 3a(n-1).

Pisot sequence E(x, y): a(0) = x, a(1) = y, a(n) = roundUp(a(n-1)^2/a(n-2)) = [ a(n-1)^2/a(n-2) + 1/2 ].

Pisot sequence L(x, y): a(0) = x, a(1) = y, a(n) = ceiling(a(n-1)^2/a(n-2)).

Pisot sequence P(x, y): a(0) = x, a(1) = y, a(n) = roundDown(a(n-1)^2/a(n-2)) = ceiling(a(n-1)^2/a(n-2) - 1/2).

Pisot sequence T(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)) = [ a(n-1)^2/a(n-2) ].

G.f.: 2/(1-3x) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 08 2007

a(n)=EulerPhi[3^n] [From Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008]

E.g.f.: 2*e^(3*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 15 2009]

with(finance):seq(futurevalue(2, 2, n), n=0..27); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]

with(finance):seq(futurevalue(6, 2, n), n=-1..26); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]

Table[EulerPhi[3^n], {n, 0, 100}] [From Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008]

Apart from initial term, same as A025192. Cf. A080643.

Sequence in context: A072852 A072853 A025192 this_sequence A134635 A114464 A062415

Adjacent sequences: A008773 A008774 A008775 this_sequence A008777 A008778 A008779

easy,nonn

N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)