%I #17 Feb 05 2023 09:13:50
%S 79,527,2415,9263,31871,101759,307455,890111,2490367,6774783,18001919,
%T 46886911,120029183,302678015,753205247,1852375039,4507828223,
%U 10866393087,25970081791,61583917055,144997089279,339159810047
%N 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.
%C 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.
%D 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.
%H Venkat Murali, <a href="https://www.ru.ac.za/mathematics/people/staff/venkatmurali/">Home page</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-50,120,-160,112,-32).
%F a(n) = 2^(n+1)*( (n^4 + 23*n^3)/6 + (79*n^2 + 185*n)/3 + 40 ) - 1.
%F 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]
%e 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.
%t a[n_] := 2^n(n^4 + 23n^3 + 158n^2 + 370n + 240)/3 - 1; Table[ a[n], {n, 0, 21}] (* _Robert G. Wilson v_, May 31 2005 *)
%Y Cf. A007047, A107392, A107464, A107953.
%K easy,nonn
%O 0,1
%A Venkat Murali (v.murali(AT)ru.ac.za), May 30 2005
%E a(6)-a(21) from _Robert G. Wilson v_, May 31 2005