cp's OEIS Frontend

A107955 Number of chains in the power set lattice or the number of fuzzy subsets of an (n+5)-element set X_(n+5) with specification n elements of one kind, 4 elements of another and 1 of yet another kind.

%I A107955 #17 Feb 05 2023 09:20:44
%S A107955 191,1471,7551,31871,119231,410303,1327103,4090623,12130303,34842623,
%T A107955 97435647,266313727,713637887,1879523327,4875091967,12474187775,
%U A107955 31531728895,78832992255,195135799295,478649778175,1164351373311
%N A107955 Number of chains in the power set lattice or the number of fuzzy subsets of an (n+5)-element set X_(n+5) with specification n elements of one kind, 4 elements of another and 1 of yet another kind.
%C A107955 This sequence is another example, together with A107953 and A107954, of a triple sequence A(n,m,l) with n a nonnegative integer, m = 4 and l = 1.
%D A107955 Venkat Murali, On the enumeration of fuzzy subsets of an (n+5)-element set X_(n+5) of specification n^1 4^1 1, Rhodes University JRC-Abstract-Report, In Preparation, 15 pages 2005.
%H A107955 Venkat Murali, <a href="https://www.ru.ac.za/mathematics/people/staff/venkatmurali/">Home page</a>.
%H A107955 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (13,-72,220,-400,432,-256,64).
%F A107955 a(n) = (2^(n+1))*(1/24)*(n^5 + 36*n^4 + 431*n^3 + 2088*n^2 + 3972*n + 2304) - 1,
%F A107955 G.f.: (320*x^5-1360*x^4+2400*x^3-2180*x^2+1012*x-191) / ((x-1)*(2*x-1)^6). [_Colin Barker_, Dec 10 2012]
%e A107955 a(3) = (2^(3+1))*(1/24)*(3^5 + 36 * 3^4 + 431 * 3^3 + 2088 * 3^2 + 3972 * 3 + 2304) - 1 = 31871. This is the number of chains in the power set lattice (which is also the number of fuzzy subsets) of X_(n+5).
%Y A107955 Cf. A007047, A107392, A107464, A107953, A107954.
%K A107955 easy,nonn
%O A107955 0,1
%A A107955 Venkat Murali (v.murali(AT)ru.ac.za), Jun 01 2005