A361963 Total number of 3-Fuss-skew paths of semilength n

4, 64, 1296, 29888, 745856, 19614464, 535394560, 15026146304, 430901082112, 12570964738048, 371918487789568, 11132402289049600, 336515403043962880, 10258388252467200000, 315006202191320514560, 9734768426532836474880, 302531413305855206490112, 9448885107650550229368832

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Toufik Mansour, Jose Luis Ramirez, Enumration of Fuss-skew paths, Ann. Math. Inform. 55 (2022) 125-136, table 1, l=3.

Formula

D-finite with recurrence 3*n*(835563*n-1169848) *(3*n-1) *(3*n+1) *a(n) +(-677815401*n^4 +1413824080*n^3 -54384639*n^2 -1200906664*n +537620544) *a(n-1) +(-3193018081*n^4 +33631350714*n^3 -117976832747*n^2 +171281820906*n -88774504872) *a(n-2) +(n-3) *(6267356473*n^3 -46526529435*n^2 +108917381042*n -78511581720) *a(n-3) -20*(4542739*n -6358171) *(n-3) *(n-4) *(2*n-7)*a(n-4)=0.

Maple

FussSkew := 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)
        * 3^k*2^(n*(l-2)+2*j-k+1), k=0..j) ;
    end do:
    a/n ;
end proc:
seq(FussSkew(3, n), n=1..40) ;

Crossrefs

Cf. A002212 (1-Fuss-skew), A361962 (2-Fuss-skew)

Sequence in context: A014729 A322519 A259272 * A085532 A371661 A352275

Adjacent sequences: A361960 A361961 A361962 * A361964 A361965 A361966

Keyword

nonn,easy

Author

R. J. Mathar, Mar 31 2023

Status

approved