A361965 Total number of peaks in 3-Fuss-skew paths of semilength n.

4, 96, 2672, 78848, 2400896, 74568704, 2347934464, 74675511296, 2393372833792, 77176031297536, 2500887165493248, 81372026697351168, 2656708513978580992, 86992366046604165120, 2855701159218522030080, 93950313500933860884480, 3096866628586659248603136

Offset: 1

Author

R. J. Mathar, Mar 31 2023

Keywords

• nonn
• easy

Links

• Toufik Mansour, Jose Luis Ramirez, Enumration of Fuss-skew paths, Ann. Math. Inform. 55 (2022) 125-136, table 2, l=3.

Crossrefs

Cf. A026378 (1-Fuss-skew), A361964 (2-Fuss-skew)

Programs

Maple

FussSkewP := proc(l,n)
    local a,j,k ;
    a := 0 ;
    for j from 0 to n do
        a := a+sum( binomial(n,j) *binomial(j,k) *binomial(n*(l-1),n-2*j+k-1)
        * 2^(n*(l-2)+2*j-k+1)*3^(k-1)*(3*(n-j)+k),k=0..j) ;
    end do:
    a/n ;
end proc:
seq(FussSkewP(3,n),n=1..40) ;