A361964 Total number of peaks in 2-Fuss-skew paths of semilength n.

2, 20, 226, 2696, 33138, 415164, 5270850, 67576208, 872918690, 11343392228, 148120453538, 1941910368280, 25545250484498, 337010368660876, 4457154741645954, 59076597464830240, 784518823873380930, 10435840680299248052, 139030100339736030306, 1854730153008453738408

Offset: 1

Author

R. J. Mathar, Mar 31 2023

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A026378 (1-Fuss-skew), A361965 (3-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(2,n),n=1..40) ;

Formula

D-finite with recurrence 2*n *(2*n-1) *(98653*n-203080) *a(n) +(-5301667*n^3 [phone]*n^2 -3506028*n -3685230) *a(n-1) +(-1931311*n^3 [phone]*n^2 -151212227*n [phone]) *a(n-2) +(n-3)*(8016735*n^2 -44290066*n [phone]) *a(n-3) +5*(n-3) *(n-4) *(129715*n-300617) *a(n-4)=0.