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%I #24 Apr 16 2023 10:42:10
%S 2,5,17,57,185,593,1901,6121,19793,64161,208085,674105,2179001,
%T 7023409,22566269,72268809,230696609,734153537,2329503653,7371475033,
%U 23267249417,73268609745,230224239437,721965697577,2259855722225
%N Number of idempotents in Identity Difference Partial Transformation semigroup.
%C 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.
%C #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.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,-58,144,-193,132,-36).
%F #IDP_n = (n-1)*3^(n-2) + n*2^(n-1) - n + 2.
%F 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
%e Example: For n=4, #IDP_n = 3*9 + 4*8 - 4 + 2 = 27 + 32 - 2 = 57
%t LinearRecurrence[{12,-58,144,-193,132,-36},{2,5,17,57,185,593},30] (* _Harvey P. Dale_, Apr 11 2020 *)
%Y Cf. A189890.
%K nonn
%O 1,1
%A _Adeniji, Adenike_, Jun 04 2011
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