0,4

Also, number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004

No multiplications, no exponentiation is required! Simplify! [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Gessel and R. P. Stanley, Stirling polynomials, J. Combin. Theory, A 24 (1978), 24-33.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 256.

Klavzar, S.; Milutinovic, U.; and Petr, C., Hanoi graphs and some classical numbers, Expo. Math. 23 (2005), no. 4, 371-378.

T. D. Noe, Table of n, a(n) for n=0..500

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).

G.f.: 1 + 2x^3/((1-x)^2(1-2x)). a(n)=A008517(n-1, 2). - Michael Somos, Oct 13, 2002

Equals binomial transform of [1, -1, 1, 1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2008

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

a(0) = 1 and a(n) = sum((-1)^(n+k+1)*binomial(2*n-1,k)*stirling1(2*n-k-3,n-k-2),k=0..n-3), n=>1.

(End)

a:=n->sum (2^j-2, j=2..n): seq(a(n), n=-1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007

A005803:=-2*z/(2*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence except for three leading terms.]

lst={1, 0}; s=0; Do[s+=(s+=n); AppendTo[lst, s], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]

(PARI) a(n)=if(n<0, 0, 2^n-2*n)

a(n) = A070313 + 1 = A052515 + 2. Bisection of A077866.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

Equals for n =>3 the third right hand column of A163936.

(End)

Sequence in context: A006696 A094939 A006732 this_sequence A145654 A074352 A017928

Adjacent sequences: A005800 A005801 A005802 this_sequence A005804 A005805 A005806

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)