A361960 Total semiperimeter of 2-Fuss-Catalan polyominoes of length 2n.
2, 12, 71, 430, 2652, 16576, 104652, 665874, 4263050, 27430260, 177233355, 1149159336, 7473264736, 48725661120, 318403991656, 2084753927898, 13673789668854, 89825336129620, 590901795716925, 3892055708986830, 25664871706721940, 169414775012098560, 1119378775384200240, 7402571891557073400, 48993463632294517752, 324501821324483687856
Offset: 1
Links
- Toufik Mansour, I. L. Ramirez, Enumerations of polyominoes determined by Fuss-Catalan words, Australas. J. Combin. 81 (3) (2021) 447-457, Table 2
Programs
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Maple
Per := proc(s,p,n) local i,j,a ; a := 0 ; for i from 0 to n-1 do for j from 0 to n-1-i do a := a+ (-1)^j*p^(n+1+i+(s+1)*j) *binomial(n-1+i,i)*binomial(n,j)*binomial(n+s*j,n-1-i-j)/(1-p)^(i+j) ; end do: end do: expand(a/n) ; factor(%) ; end proc: Per1std := proc(s,n) local p; Per(s,p,n) ; diff(%,p) ; factor(%) ; subs(p=1,%) ; end proc: seq(Per1std(2,n),n=1..30) ;
Formula
Conjecture: D-finite with recurrence 4*n*(2*n+1)*a(n) -6*n*(11*n-5)*a(n-1) +3*(43*n^2-169*n+130)*a(n-2) -36*(3*n-8)*(3*n-10)*a(n-3)=0.