1,1

Number of walks of length 2n+8 in the path graph P_9 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/(1-8x+21x^2-20x^3+5x^4) - 1. a(n)=8a(n-1)-21a(n-2)+20a(n-3)-5a(n-4). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2004

a(k)=sum(binomial(8+2k, 10j+k-2)-binomial(8+2k, 10j+k-1), j=-infinity..infinity) (a finite sum).

a:=k->sum(binomial(8+2*k, 10*j+k-2), j=ceil((2-k)/10)..floor((10+k)/10))-sum(binomial(8+2*k, 10*j+k-1), j=ceil((1-k)/10)..floor((9+k)/10)): seq(a(k), k=1..28);

A005024:=-(-8+21*z-20*z**2+5*z**3)/(5*z**2-5*z+1)/(z**2-3*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

Sequence in context: A000429 A055853 A137748 this_sequence A094865 A122880 A099253

Adjacent sequences: A005021 A005022 A005023 this_sequence A005025 A005026 A005027

nonn,walk

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