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

1,1

Links

Table of n, a(n) for n=1..20.

Toufik Mansour and José Luis Ramírez, Enumeration of Fuss-skew paths, Ann. Math. Inform. 55 (2022) 125-136, table 2, l=2.

Formula

D-finite with recurrence 2*n *(2*n-1) *(98653*n-203080) *a(n) +(-5301667*n^3 +13746049*n^2 -3506028*n -3685230) *a(n-1) +(-1931311*n^3 +43294062*n^2 -151212227*n +137614530) *a(n-2) +(n-3)*(8016735*n^2 -44290066*n +61812586) *a(n-3) +5*(n-3) *(n-4) *(129715*n-300617) *a(n-4)=0.

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) ;

Crossrefs

Cf. A026378 (1-Fuss-skew), A361965 (3-Fuss-skew).

Sequence in context: A214769 A227337 A127110 * A337856 A296660 A197898

Adjacent sequences: A361961 A361962 A361963 * A361965 A361966 A361967

Keyword

easy,nonn

Author

R. J. Mathar, Mar 31 2023

Status

approved