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A361960
Total semiperimeter of 2-Fuss-Catalan polyominoes of length 2n.
1
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
1,1
LINKS
Toufik Mansour, I. L. Ramirez, Enumerations of polyominoes determined by Fuss-Catalan words, Australas. J. Combin. 81 (3) (2021) 447-457, Table 2
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.
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) ;
CROSSREFS
Cf. A024482 (1-Fuss-Catalan), A075045 (total area), A361961 (3-Fuss-Catalan).
Sequence in context: A012381 A012376 A223763 * A002630 A009552 A002670
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 31 2023
STATUS
approved