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 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. 0
 191, 1471, 7551, 31871, 119231, 410303, 1327103, 4090623, 12130303, 34842623, 97435647, 266313727, 713637887, 1879523327, 4875091967, 12474187775, 31531728895, 78832992255, 195135799295, 478649778175, 1164351373311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. REFERENCES 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. LINKS Table of n, a(n) for n=0..20. Venkat Murali, Home page. Index entries for linear recurrences with constant coefficients, signature (13,-72,220,-400,432,-256,64). FORMULA a(n) = (2^(n+1))*(1/24)*(n^5 + 36*n^4 + 431*n^3 + 2088*n^2 + 3972*n + 2304) - 1, 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] EXAMPLE 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). CROSSREFS Cf. A007047, A107392, A107464, A107953, A107954. Sequence in context: A142451 A083980 A144327 * A264844 A061331 A177683 Adjacent sequences: A107952 A107953 A107954 * A107956 A107957 A107958 KEYWORD easy,nonn AUTHOR Venkat Murali (v.murali(AT)ru.ac.za), Jun 01 2005 STATUS approved

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Last modified September 28 07:34 EDT 2023. Contains 365724 sequences. (Running on oeis4.)