A107953 -id:A107953 - cp's OEIS frontend

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.

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

Offset: 0

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

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.

			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.

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.

Venkat Murali, Home page.
Index entries for linear recurrences with constant coefficients, signature (11,-50,120,-160,112,-32).

Cf. A007047, A107392, A107464, A107953.

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 *)
LinearRecurrence[{11,-50,120,-160,112,-32},{79,527,2415,9263,31871,101759},40] (* Harvey P. Dale, Aug 15 2025 *)

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]

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

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.

Original entry on oeis.org

191, 1471, 7551, 31871, 119231, 410303, 1327103, 4090623, 12130303, 34842623, 97435647, 266313727, 713637887, 1879523327, 4875091967, 12474187775, 31531728895, 78832992255, 195135799295, 478649778175, 1164351373311

Offset: 0

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

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.

			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).

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 JRC-Abstract-Report, In Preparation, 15 pages 2005.

Venkat Murali, Home page.
Index entries for linear recurrences with constant coefficients, signature (13,-72,220,-400,432,-256,64).

Cf. A007047, A107392, A107464, A107953, A107954.

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^5-1360*x^4+2400*x^3-2180*x^2+1012*x-191) / ((x-1)*(2*x-1)^6). [Colin Barker, Dec 10 2012]

cp's OEIS Frontend

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.

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