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A190531 Number of idempotents in Identity Difference Partial Transformation semigroup. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A180148 A241133 A148410 * A148411 A149987 A149988

Adjacent sequences:  A190528 A190529 A190530 * A190532 A190533 A190534

KEYWORD

nonn

AUTHOR

Adeniji, Adenike, Jun 04 2011

STATUS

approved

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Last modified May 18 13:13 EDT 2022. Contains 353815 sequences. (Running on oeis4.)