A190531 Number of idempotents in Identity Difference Partial Transformation semigroup.

2, 5, 17, 57, 185, 593, 1901, 6121, 19793, 64161, 208085, 674105, 2179001, 7023409, 22566269, 72268809, 230696609, 734153537, 2329503653, 7371475033, 23267249417, 73268609745, 230224239437, 721965697577, 2259855722225

Offset

1,1

Comments

IDP_n is a semigroup with the non-isolation property and E(IDP_n) denotes the set of idempotents (satisfying e^2 = e) in IDP_n.

#E(IDP_n) is the number of idempotent elements in the semigroup IDP_n for each n in N. E(IDP_n) is a subset of partial transformation semigroup having the property that the difference in the image, Im(alpha), is not greater than 1 and e^2 = e for each e in IDP_n.

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (12,-58,144,-193,132,-36).

Formula

#IDP_n = (n-1)*3^(n-2) + n*2^(n-1) - n + 2.

G.f.: -x*(-2+19*x-73*x^2+145*x^3-153*x^4+68*x^5) / ( (x-1)^2*(3*x-1)^2*(2*x-1)^2 ). - R. J. Mathar, Jun 19 2011

Example

Example: For n=4, #IDP_n = 3*9 + 4*8 - 4 + 2 = 27 + 32 - 2 = 57

Mathematica

LinearRecurrence[{12, -58, 144, -193, 132, -36}, {2, 5, 17, 57, 185, 593}, 30] (* Harvey P. Dale, Apr 11 2020 *)

Crossrefs

Cf. A189890.

Sequence in context: A378571 A241133 A148410 * A148411 A149987 A149988

Adjacent sequences: A190528 A190529 A190530 * A190532 A190533 A190534

Keyword

nonn

Author

Adeniji, Adenike, Jun 04 2011

Status

approved