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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 (list; graph; refs; listen; history; text; internal format)
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 JRC-Abstract-Report, 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^4-432*x^3+568*x^2-342*x+79) / ((x-1)*(2*x-1)^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

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)