0,1

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.

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).

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(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.

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 *)

Cf. A007047, A107392, A107464, A107953.

Sequence in context: A142618 A248819 A141563 * A098673 A056211 A139184

Adjacent sequences: A107951 A107952 A107953 * A107955 A107956 A107957

easy,nonn

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

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

approved