

A107954


Number of chains in the power set lattice, or the number of fuzzy subsets of an (n+4)element set X_(n+4) with specification n elements of one kind, 3 elements of another and 1 of yet another kind.


1



79, 527, 2415, 9263, 31871, 101759, 307455, 890111, 2490367, 6774783, 18001919, 46886911, 120029183, 302678015, 753205247, 1852375039, 4507828223, 10866393087, 25970081791, 61583917055, 144997089279, 339159810047
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OFFSET

0,1


COMMENTS

This sequence is an example of another line in a triple sequence A(n,m,l) with n a nonnegative integer, m = 2 and l = 1. It is related to sequences A107464, A107953 which are part of the same triple sequence with different parameter values for m and l.


REFERENCES

V. Murali, On the enumeration of fuzzy subsets of X_(n+4) of specification n^1 3^1 1, Rhodes University JRCAbstractReport, In Preparation, 12 pages 2005.


LINKS

Table of n, a(n) for n=0..21.
V. Murali, FSRG Rhodes University.
Index entries for linear recurrences with constant coefficients, signature (11,50,120,160,112,32).


FORMULA

a(n) = 2^(n+1)*( (n^4 + 23 n^3)/6 + (79 n^2 + 185 n)/3 + 40 )  1.
G.f.: (128*x^4432*x^3+568*x^2342*x+79) / ((x1)*(2*x1)^5). [Colin Barker, Dec 10 2012]


EXAMPLE

a(2) = 8 * ( (16 + 184)/6 + (316 + 370)/3 + 40 )  1 = 2415. This is the number of fuzzy subsets of a set of (2+4) elements of which 2 are of one kind, 3 are of another kind and 1 of a kind distinct from the other two.


MATHEMATICA

f[n_] := 2^n(n^4 + 23n^3 + 158n^2 + 370n + 240)/3  1; Table[ f[n], {n, 0, 21}] (* Robert G. Wilson v, May 31 2005 *)


CROSSREFS

Cf. A007047, A107392, A107464, A107953.
Sequence in context: A142618 A248819 A141563 * A098673 A056211 A139184
Adjacent sequences: A107951 A107952 A107953 * A107955 A107956 A107957


KEYWORD

easy,nonn


AUTHOR

Venkat Murali (v.murali(AT)ru.ac.za), May 30 2005


EXTENSIONS

a(6)a(21) from Robert G. Wilson v, May 31 2005


STATUS

approved



