1,2

This is an application of the general formula that Paul Barry gives for sequence A000129 to the subsequence of odd-indexed terms. - Pat Costello (pat.costello(AT)eku.edu), May 20 2003

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.

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.

G.f.: x^2*(2+x+x^2+x^3-5*x^4)/(1-x-x^2+x^6).

a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5), n>=6.

a(n)=sum{k=0, ..n, C(2n+1, 2k+1)2^k}. - Pat Costello (pat.costello(AT)eku.edu), May 20 2003

A001635:=-z*(2+3*z+4*z**2+5*z**3)/(-1+z**2+z**3+z**4+z**5); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

(Maple) a := n -> (Matrix([[5, -1$3, 3, 4]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [1$2, 0$3, -1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=1..39); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]

(PARI) a(n)=if(n<0, 0, polcoeff(x^2*(2+x+x^2+x^3-5*x^4)/(1-x-x^2+x^6)+x*O(x^n), n))

Cf. A000129.

Adjacent sequences: A001632 A001633 A001634 this_sequence A001636 A001637 A001638

Sequence in context: A047402 A088196 A112925 this_sequence A106172 A090695 A104074

nonn

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

Edited by Michael Somos, Feb 17, 2002