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A189826
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a(n) = (3^n-n)*(n-1) - 2^n*(n-2).
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1
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2, 7, 40, 199, 856, 3359, 12440, 44335, 153808, 523159, 1752928, 5804759, 19041608, 61981807, 200458504, 644783071, 2064276256, 6581953703, 20911793168, 66230028871, 209167217752, 658918365247, 2070973772920, 6495510239759, 20334154874096, 63545035094839
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OFFSET
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1,1
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COMMENTS
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Previous name was: Identity difference partial transformation semigroup, IDP_n is obtained by taking the absolute value of the difference between the max(Im(alpha)) and min(Im(alpha)) <= 1. The number of elements for each n is denoted by #IDP_n.
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LINKS
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FORMULA
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a(n) = (3^n-n)*(n-1) - 2^n*(n-2).
G.f.: -x*(2 - 19*x + 89*x^2 - 235*x^3 + 329*x^4 - 210*x^5 + 36*x^6) / ( (3*x-1)^2 *(2*x-1)^2 *(x-1)^3 ). - R. J. Mathar, Jun 20 2011
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EXAMPLE
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For n=4, #IDP_n = 199.
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MATHEMATICA
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LinearRecurrence[{13, -70, 202, -337, 325, -168, 36}, {2, 7, 40, 199, 856, 3359, 12440}, 30] (* Harvey P. Dale, Apr 03 2016 *)
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PROG
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(PARI) a(n) = (3^n-n)*(n-1)-2^n*(n-2); \\ Altug Alkan, Sep 20 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Simpler name using formula from Joerg Arndt, Sep 20 2018
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STATUS
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approved
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