

A107953


Number of chains in the power set lattice of an (n+3)element set X_(n+3) of specification n^1 2^1 1, that is, n identical objects of one kind, 2 identical objects of another kind and one other kind. It is the same as the number of fuzzy subsets X_(n+3).


3



31, 175, 703, 2415, 7551, 22143, 61951, 167167, 438271, 1122303, 2818047, 6959103, 16941055, 40730623, 96862207, 228130815, 532676607, 1234173951, 2839543807, 6491734015, 14755561471, 33361494015, 75061264383, 168124481535, 375004332031, 833223655423
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OFFSET

0,1


COMMENTS

This sequence is one of a triple sequence A(n,m,l) of the number of fuzzy subsets of a set with n+m+l objects of 3 kinds. There are n,m and l objects for each kind respectively. Here a(n)= A(n,2,1). The sequence A107464 is one other example of A(n,m,l) for m=l=1.


REFERENCES

V. Murali, On the number of fuzzy subsets of an (n+3)element set of specification n^1 2^1 1, Rhodes University Preprint, 2005.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
V. Murali, FSRG Rhodes University .
Index entries for linear recurrences with constant coefficients, signature (9,32,56,48,16).


FORMULA

a(n) = 2^(n+1)*(((n^2)/2)(n+13) + 21n + 16)1.
G.f.: (48*x^3120*x^2+104*x31) / ((x1)*(2*x1)^4).  Colin Barker, Jan 15 2015
a(0)=31, a(1)=175, a(2)=703, a(3)=2415, a(4)=7551, a(n)=9*a(n1) 32*a(n2)+ 56*a(n3)48*a(n4)+16*a(n5).  Harvey P. Dale, Feb 10 2015


EXAMPLE

a(3) = 2^4*((9/2)*16 + 21*3 + 16)  1 = 2415 which is the number of distinct chains in the power set lattice (or fuzzy subsets) of a set X_(n+3) with 3 kinds of objects, n of one kind, 2 of another and one of yet another.


MATHEMATICA

Table[2^(n+1) (n^2/2 (n+13)+21n+16)1, {n, 0, 30}] (* or *) LinearRecurrence[ {9, 32, 56, 48, 16}, {31, 175, 703, 2415, 7551}, 30] (* Harvey P. Dale, Feb 10 2015 *)


PROG

(PARI) Vec((48*x^3120*x^2+104*x31)/((x1)*(2*x1)^4) + O(x^100)) \\ Colin Barker, Jan 15 2015


CROSSREFS

Cf. A107464, A007047, A107392.
Sequence in context: A184489 A140540 A183877 * A085249 A272130 A296959
Adjacent sequences: A107950 A107951 A107952 * A107954 A107955 A107956


KEYWORD

nice,nonn,tabl,easy


AUTHOR

Venkat Murali (v.murali(AT)ru.ac.za), May 28 2005


EXTENSIONS

a(5) corrected Jun 01 2005
Incorrect term deleted by Colin Barker, Jan 15 2015


STATUS

approved



