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.

191, 1471, 7551, 31871, 119231, 410303, 1327103, 4090623, 12130303, 34842623, 97435647, 266313727, 713637887, 1879523327, 4875091967, 12474187775, 31531728895, 78832992255, 195135799295, 478649778175, 1164351373311

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