

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
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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 JRCAbstractReport, In Preparation, 15 pages 2005.


LINKS



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^51360*x^4+2400*x^32180*x^2+1012*x191) / ((x1)*(2*x1)^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



KEYWORD

easy,nonn


AUTHOR

Venkat Murali (v.murali(AT)ru.ac.za), Jun 01 2005


STATUS

approved



