1,1

Number of walks of length 2n+9 in the path graph P_10 from one end to the other one. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 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.

Everett, C. J.; Stein, P. R.; The combinatorics of random walk with absorbing barriers. Discrete Math. 17 (1977), no. 1, 27-45.

W. Feller, An Introduction to Probability Theory and its Applications, 3rd ed, Wiley, New York, 1968, p. 96

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.=1/(1-9x+28x^2-35x^3+15x^4-x^5) - 1. a(n)=9a(n-1)-28a(n-2)+35a(n-3)-15a(n-4)+a(n-5). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2004

a(k)=sum(binomial(9+2k, 11j+k-2)-binomial(9+2k, 11j+k-1), j=-infinity..infinity) (a finite sum).

a:=k->sum(binomial(9+2*k, 11*j+k-2), j=ceil((2-k)/11)..floor((11+k)/11))-sum(binomial(9+2*k, 11*j+k-1), j=ceil((1-k)/11)..floor((10+k)/11)): seq(a(k), k=1..28);

A005025:=-(9-28*z+35*z**2-15*z**3+z**4)/(-1+9*z-28*z**2+35*z**3-15*z**4+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]

Sequence in context: A126085 A055854 A122588 this_sequence A038761 A003698 A001688

Adjacent sequences: A005022 A005023 A005024 this_sequence A005026 A005027 A005028

nonn,walk

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