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A361965 Total number of peaks in 3-Fuss-skew paths of semilength n.

%I A361965 #6 Jul 23 2025 16:04:40
%S A361965 4,96,2672,78848,2400896,74568704,2347934464,74675511296,
%T A361965 2393372833792,77176031297536,2500887165493248,81372026697351168,
%U A361965 2656708513978580992,86992366046604165120,2855701159218522030080,93950313500933860884480,3096866628586659248603136
%N A361965 Total number of peaks in 3-Fuss-skew paths of semilength n.
%H A361965 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=3.
%p A361965 FussSkewP := proc(l,n)
%p A361965     local a,j,k ;
%p A361965     a := 0 ;
%p A361965     for j from 0 to n do
%p A361965         a := a+sum( binomial(n,j) *binomial(j,k) *binomial(n*(l-1),n-2*j+k-1)
%p A361965         * 2^(n*(l-2)+2*j-k+1)*3^(k-1)*(3*(n-j)+k),k=0..j) ;
%p A361965     end do:
%p A361965     a/n ;
%p A361965 end proc:
%p A361965 seq(FussSkewP(3,n),n=1..40) ;
%Y A361965 Cf. A026378 (1-Fuss-skew), A361964 (2-Fuss-skew)
%K A361965 nonn,easy
%O A361965 1,1
%A A361965 _R. J. Mathar_, Mar 31 2023