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

Author

Adeniji, Adenike, Jun 04 2011

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A189890.

Programs

Mathematica

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

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