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

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

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

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.

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.

Sequence in context: A047402 A088196 A112925 this_sequence A106172 A090695 A104074

Adjacent sequences: A001632 A001633 A001634 this_sequence A001636 A001637 A001638

nonn

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

Edited by Michael Somos, Feb 17, 2002