1,2

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).

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.

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+x^4-6*x^5)/(1-x-x^2+x^7).

a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), n>=7.

A001636:=-z*(2+3*z+4*z**2+5*z**3+6*z**4)/(z+1)/(z**5+z**3+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

(Maple) a := n -> (Matrix([[6, -1$4, 4, 5]]). Matrix(7, (i, j)-> if (i=j-1) then 1 elif j=1 then [1$2, 0$4, -1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=1..38); [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+x^4-6*x^5)/(1-x-x^2+x^7)+x*O(x^n), n))

Cf. A013983.

Adjacent sequences: A001633 A001634 A001635 this_sequence A001637 A001638 A001639

Sequence in context: A066895 A105075 A140669 this_sequence A036588 A099517 A026647

nonn

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

Edited by Michael Somos, Feb 17, 2002