0,3

Number of alignments of n strings of length 3.

Joseph B. Slowinski, The Number of Multiple Alignments, Molecular Phylogenetics and Evolution, Volume 10, Issue 2, October 1998, Pages 264-266.

A000629 := proc(n) local k ; sum( k^n/2^k, k=0..infinity) ; end: A062208 := proc(n) local a, stir, ni, n1, n2, n3, stir2, i, j, tmp ; a := 0 ; if n = 0 then RETURN(1) ; fi ; stir := combinat[partition](n) ; stir2 := {} ; for i in stir do if nops(i) <= 3 then tmp := i ; while nops(tmp) < 3 do tmp := [op(tmp), 0] ; od: tmp := combinat[permute](tmp) ; for j in tmp do stir2 := stir2 union { j } ; od: fi ; od: for ni in stir2 do n1 := op(1, ni) ; n2 := op(2, ni) ; n3 := op(3, ni) ; a := a+combinat[multinomial](n, n1, n2, n3)*(A000629(3*n1+2*n2+n3)-1/2-2^(3*n1+2*n2+n3)/4)*(-3)^n2*2^n3 ; od: a/(2*6^n) ; end: seq(A062208(n), n=0..14) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2008

a:=proc(n) options operator, arrow: sum(binomial(m, 3)^n*2^(-m-1), m=0.. infinity) end proc: seq(a(n), n=0..12); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 22 2008

Cf. A000670, A055203, A001850, A126086.

See A062204 for further references, formulas and comments.

Cf. A001850, A062204, A062205.

Sequence in context: A046190 A093263 A069433 this_sequence A132594 A001238 A110852

Adjacent sequences: A062205 A062206 A062207 this_sequence A062209 A062210 A062211

nonn

Angelo Dalli (adal002(AT)um.edu.mt), Jun 13 2001

New definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 01 2008

Edited by N. J. A. Sloane, Sep 19 2009 at the suggestion of Max Alekseyev