0,5

a(n+1)=S(n) for n>=1, where S(n) is the number of 01-words of length n, having first letter 1, in which all runlengths of 1's are odd. Example: S(4) counts 1000,1001,1010,1110. See A077865. - Clark Kimberling (ck6(AT)evansville.edu), Jun 26 2004

Counts walks of length n between the first and second nodes of P_3, to which a loop has been added at the end. Let A be the adjacency matrix of the graph P_3 with a loop added at the end. A is a 'reverse Jordan matrix' [0,0,1;0,1,1;1,1,0]. a(n) is obtained by taking the (1,2) element of A^n. - Paul Barry (pbarry(AT)wit.ie), Jul 16 2004

Interleaves A094790 and A094789. - Paul Barry (pbarry(AT)wit.ie), Oct 30 2004

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

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.

R. Chapman, Eigenvalues of a Bidiagonal Matrix, Amer. Math. Monthly, 111 (2004) p. 441

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 433

a(n+2)=A094790(n/2+1)(1+(-1)^n)/2+A094789((n+1)/2)(1-(-1)^n)/2 - Paul Barry (pbarry(AT)wit.ie), Oct 30 2004

First differences of A028495. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 02 2005

G.f.=x^2/(1-x-2x^2+x^3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2004

a[0]:=0: a[1]:=0: a[2]:=1: for n from 3 to 40 do a[n]:=a[n-1]+2*a[n-2]-a[n-3] od:seq(a[n], n=0..40); (Deutsch)

A006053:=z**2/(1-z-2*z**2+z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A096975, A096976.

Sequence in context: A014596 A002823 A109509 this_sequence A051841 A096081 A054162

Adjacent sequences: A006050 A006051 A006052 this_sequence A006054 A006055 A006056

nonn,easy

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

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2004