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

%I A361964 #7 Jul 23 2025 16:04:35
%S A361964 2,20,226,2696,33138,415164,5270850,67576208,872918690,11343392228,
%T A361964 148120453538,1941910368280,25545250484498,337010368660876,
%U A361964 4457154741645954,59076597464830240,784518823873380930,10435840680299248052,139030100339736030306,1854730153008453738408
%N A361964 Total number of peaks in 2-Fuss-skew paths of semilength n.
%H A361964 Toufik Mansour, Jose Luis Ramirez, <a href="https://doi.org/10.33039/ami.2022.01.002">Enumration of Fuss-skew paths</a>, Ann. Math. Inform. 55 (2022) 125-136, table 2, l=2.
%F A361964 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.
%p A361964 FussSkewP := proc(l,n)
%p A361964     local a,j,k ;
%p A361964     a := 0 ;
%p A361964     for j from 0 to n do
%p A361964         a := a+sum( binomial(n,j) *binomial(j,k) *binomial(n*(l-1),n-2*j+k-1)
%p A361964         * 2^(n*(l-2)+2*j-k+1)*3^(k-1)*(3*(n-j)+k),k=0..j) ;
%p A361964     end do:
%p A361964     a/n ;
%p A361964 end proc:
%p A361964 seq(FussSkewP(2,n),n=1..40) ;
%Y A361964 Cf. A026378 (1-Fuss-skew), A361965 (3-Fuss-skew)
%K A361964 easy,nonn
%O A361964 1,1
%A A361964 _R. J. Mathar_, Mar 31 2023