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