cp's OEIS Frontend

A278025 Number of irreducible involutions of length n avoiding the pattern {123}.

%I A278025 #25 Jan 31 2024 08:03:39
%S A278025 1,3,4,9,16,31,58,112,211,411,781,1526,2923,5721,11023,21610,41821,
%T A278025 82112,159460,313503,610531,1201721,2345734,4621899,9039472,17827054,
%U A278025 34923997,68930585,135231649,267104311,524673184,1036989265,2039191564,4032728190,7937870407
%N A278025 Number of irreducible involutions of length n avoiding the pattern {123}.
%H A278025 Robert Israel, <a href="/A278025/b278025.txt">Table of n, a(n) for n = 1..3323</a>
%H A278025 J.-L. Baril, <a href="https://doi.org/10.46298/dmtcs.2158">Avoiding patterns in irreducible permutations</a>, Discrete Mathematics and Theoretical Computer Science, Vol 17, No 3 (2016). See Table 4.
%F A278025 G.f.: ((1 + 2*x)*sqrt(1 - 4*x^2) - 1 + 4*x^2 - 2*x^3 + 2*x^4 + 4*x^5 )/((1 - 2*x)*(2*x^4 + 1 + sqrt(1 - 4*x^2))). - From Baril, corrected by _Robert Israel_, Jul 23 2020.
%p A278025 f:= gfun:-rectoproc({(20 + 4*n)*a(n) + (-54 - 8*n)*a(1 + n) + (25 + 3*n)*a(n + 2) + (64 + 6*n)*a(n + 3) + (11 + 3*n)*a(n + 4) + (-67 - 9*n)*a(n + 5) + (45 + 7*n)*a(n + 6) + (10 - 2*n)*a(n + 7) + (2*n + 16)*a(n + 8) + (51 + 5*n)*a(n + 9) + (-9 - n)*a(n + 10) + (-13 - n)*a(n + 11), a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 4, a(4) = 9, a(5) = 16, a(6) = 31, a(7) = 58, a(8) = 112, a(9) = 211, a(10) = 411, a(11) = 781},a(n),remember):
%p A278025 map(f, [$1..50]); # _Robert Israel_, Jul 23 2020
%Y A278025 Cf. A278024.
%K A278025 nonn
%O A278025 1,2
%A A278025 _N. J. A. Sloane_, Nov 09 2016
%E A278025 More terms from _Lars Blomberg_, Nov 11 2016